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conflict in equation names in Section and main fil...

Asked by: PinheiroRJ 5
worksheet editing
November 14 2024
1  9

How to insert a file inside another file, creating a session, without equations with the same name conflicting?

How to solve this equation?...

Asked by: mary120 65
solve real
November 03 2024
0  3

Hi,
I have an equation and I want to solve it parametrically to find x , but I couldn't do that with "solve" command. (I know x should be  real and positive). What should I do?
Root_of.mw

Apply Keller Box method for ODE...

Asked by: KIRAN SAJJAN 40
ode homework numeric
February 20 2024
0  2

Dear sir ,

I have implemented Dsolve method the code was executed, but i need to apply Kellor Box method to solve the ODES 

Please can any one help how to implement? 

because there is no post regarding the Kellor box method. 

> 

restart; with(plots)
> 

``
> 

S := 1; Rd := .1; delta := .1; Hs := 1; Sc := .1; Pr := 6.8; n := 1; Rc := .1; E := .1; M := 1
> 

NULL
 
> 

OdeSys := a1*(diff(f(eta), eta, eta, eta, eta))/a2-S*(3*(diff(f(eta), eta, eta))+eta*(diff(f(eta), eta, eta, eta))+(diff(f(eta), eta))*(diff(f(eta), eta, eta))-f(eta)*(diff(f(eta), eta, eta, eta)))-a5*M*(diff(f(eta), eta, eta))/a2-a1*Kp*(diff(f(eta), eta, eta))/a2 = 0, (a4+4*Rd)*(diff(Theta(eta), eta, eta))+12*Rd*delta*((diff(Theta(eta), eta))*(diff(Theta(eta), eta))+Theta(eta)*(diff(Theta(eta), eta, eta)))+Hs*Theta(eta)-a3*Pr*S*(diff(Theta(eta), eta))*(eta-f(eta)) = 0, diff(Phi(eta), eta, eta)-S*Sc*(diff(Phi(eta), eta))*(eta-f(eta))-Sc*Rc*(1+delta*Theta(eta))^n*Phi(eta)*exp(-E/(1+delta*Theta(eta))) = 0; Cond := f(0) = 0, ((D@@2)(f))(0) = 0, (D(Theta))(0) = 0, (D(Phi))(0) = 0, f(1) = 1, (D(f))(1) = 0, Theta(1) = 1, Phi(1) = 1
   
> 

KpVals := [1, 2, 3, 4]
> 

for j to numelems(KpVals) do Ans[j] := dsolve(eval([OdeSys, Cond], Kp = KpVals[j]), numeric, output = listprocedure) end do
> 

 
> 

with(plots):
 cols := [red, blue, black,green]:

 plotA:= display
  ( [ seq
      ( odeplot
        ( Ans[k],[eta,(f(eta))],
          eta=0..1,
          color=cols[k]
        ),
        k=1..numelems(KpVals)
      )
    ],linestyle = "solid",
    'axes'= 'boxed',labels=[eta,'f(eta)'],labelfont=[TIMES,BOLD,16]
  );
 
> 

with(plots):
  cols := [red, blue, black,green]:

plotB:= display( [ seq( odeplot
        ( Ans[k],[eta,Theta(eta)],
          eta=0..1,
          color=cols[k]
        ),
        k=1..numelems(KpVals)
      )
    ],linestyle = "solid",
    'axes'= 'boxed',labels=[eta,'Phi(eta)'],labelfont=[TIMES,BOLD,16]
  );

 

 
> 

with(plots):
  cols := [red, blue, black,green]:

plotC:= display( [ seq( odeplot
        ( Ans[k],[eta,Phi(eta)],
          eta=0..1,
          color=cols[k]
        ),
        k=1..numelems(KpVals)
      )
    ],linestyle = "solid",
    'axes'= 'boxed',labels=[eta,'Phi(eta)'],labelfont=[TIMES,BOLD,16]
  );

 
> 

with(plots):
 cols := [red, blue, black,green]:

 plotA:= display
  ( [ seq
      ( odeplot
        ( Ans[k],[eta,(diff(f(eta),eta))],
          eta=0..1,
          color=cols[k]
        ),
        k=1..numelems(KpVals)
      )
    ],linestyle = "solid",
    'axes'= 'boxed',labels=[eta,"f '(eta)"],labelfont=[TIMES,BOLD,16]
  );
> 

 

 
> 

 

Download kellor_box_method.mw

How to solve this Eq. by Maple?...

Asked by: raj2018 50
ode homework dsolve
February 14 2024
0  5

Hi,
I have a problem and I haven't been able to solve it yet. I want to solve an ordinary diffrential equation similar to
                                                                                                   (dphi/dxi)^2+2*V(phi)=0
and plot phi versus xi for a the following conditions:
1) V(phi)=dphi/dxi=0 at (phi=0,phi_m) and
2) dV(phi)/dphi=0 at phi=phi_m and 
3) d^2V(phi)/dphi^2=0 at both phi=0 and phi=phi_m.
How can I do this by Maple?(see the attached file)
w1.mw

Ode equations solution ...

Asked by: SHIVAS 35
ode homework numeric
December 15 2023
0  4

How to solve this type of ode in maple

need the value of S, Q, E

unable to plot 3d and 2d plots...

Asked by: KIRAN SAJJAN 40
ode numeric differential-equations
October 05 2023
0  3

  I am unable to draw both 3d plots sowing error please help me to solve

> 

restart:NULLNULL
> 

p1 := 0.1e-1; p2 := 0.2e-1; p3 := 0.1e-1; Px := p1+p2+p3
> 

rf := 1050; kf := .52; cpf := 3617; sigmaf := .8
> 

sigma1 := 25000; rs1 := 5200; ks1 := 6; cps1 := 670
> 

sigma2 := 59.7*10^6; rs2 := 8933; ks2 := 400; cps2 := 385
> 

sigma3 := 2380000; rs3 := 4250; ks3 := 8.9538; cps3 := 686.2
> 

NULL
> 

B1 := 1+2.5*Px+6.2*Px^2; B2 := 1+13.5*Px+904.4*Px^2; B3 := 1+37.1*Px+612.6*Px^2; B4 := (ks1+2*kf-2*Px*(kf-ks1))/(ks1+2*kf+Px*(kf-ks1)); B5 := (ks2+3.9*kf-3.9*Px*(kf-ks2))/(ks2+3.9*kf+Px*(kf-ks2)); B6 := (ks3+4.7*kf-4.7*Px*(kf-ks3))/(ks3+4.7*kf+Px*(kf-ks3))
> 

a2 := B1*p1+B2*p2+B3*p3
> 

a1 := 1-p1-p2-p3+p1*rs1/rf+p2*rs2/rf+p3*rs3/rf
> 

a3 := 1-p1-p2-p3+p1*rs1*cps1/(rf*cpf)+p2*rs2*cps2/(rf*cpf)+p3*rs3*cps3/(rf*cpf)
> 

a4 := B4*p1+B5*p2+B6*p3
> 

NULL
> 

a5 := 1+3*((p1*sigma1+p2*sigma2+p3*sigma3)/sigmaf-p1-p2-p3)/(2+(p1*sigma1+p2*sigma2+p3*sigma3)/((p1+p2+p3)*sigmaf)-((p1*sigma1+p2*sigma2+p3*sigma3)/sigmaf-p1-p2-p3))

``

``

> 



NULL
> 

ODE:=[(a2+K)*(diff(U0(eta), eta, eta))/a1-Ra*(diff(U0(eta), eta))+lambda0/a1-a5*M1^2*U0(eta)/a1+K*(diff(N0(eta), eta))/a1+la*Ra*Theta0(eta)*(1+Qc*Theta0(eta)), (a2+K)*(diff(U1(eta), eta, eta))/a1-H^2*l1*U1(eta)-Ra*(diff(U1(eta), eta))+lambda1/a1-a5*M1^2*U1(eta)/a1+K*(diff(N1(eta), eta))/a1+la*Ra*(Theta1(eta))(1+2*Qc*Theta0(eta)), diff(N0(eta), eta, eta)-Ra*a1*Pj*(diff(N0(eta), eta))-2*n1*N0(eta)-n1*(diff(U0(eta), eta)), diff(N1(eta), eta, eta)-Ra*a1*Pj*(diff(N1(eta), eta))-2*n1*N1(eta)-n1*(diff(U1(eta), eta))-H^2*a1*Pj*l1*N1(eta), (a4/(a3*Pr)-delta*Ra^2/H^2+4*Rd*(1+(Tp-1)^3*Theta0(eta)^3+3*(Tp-1)^2*Theta0(eta)^2+(3*(Tp-1))*Theta0(eta))/(3*a3*Pr))*(diff(Theta0(eta), eta, eta))-Ra*(diff(Theta0(eta), eta))+a5*Ec*M1^2*U0(eta)^2/a3+(a2+K)*Ec*(diff(U0(eta), eta))^2/a1+Q*Theta0(eta)/a3+4*(diff(Theta0(eta), eta))^2*Rd*(3*(Tp-1)+6*(Tp-1)^2*Theta0(eta)+3*(Tp-1)^3*Theta0(eta)^2)/(3*a3*Pr), (a4/(a3*Pr)-delta*Ra^2/H^2+4*Rd*(1+(Tp-1)^3*Theta0(eta)^3+3*(Tp-1)^2*Theta0(eta)^2+(3*(Tp-1))*Theta0(eta))/(3*a3*Pr))*(diff(Theta1(eta), eta, eta))-(H^2*l1+2*Ra*delta*l1+Ra)*(diff(Theta1(eta), eta))+(Q/a3-delta*H^2*l1^2)*Theta1(eta)+2*(a2+K)*Ec*(diff(U0(eta), eta))*(diff(U1(eta), eta))/a1+2*a5*Ec*M^2*U0(eta)*U1(eta)/a3+4*(diff(Theta0(eta), eta, eta))*Theta1(eta)*Rd*(3*(Tp-1)+6*(Tp-1)^2*Theta0(eta)+3*(Tp-1)^3*Theta0(eta)^2)/(3*a3*Pr)+4*Rd*(diff(Theta0(eta), eta))^2*(6*(Tp-1)^2*Theta1(eta)+6*(Tp-1)^3*Theta0(eta)*Theta1(eta))/(3*a3*Pr)+4*Rd*(diff(Theta1(eta), eta))*(diff(Theta0(eta), eta))*(6*(Tp-1)+6*(Tp-1)^3*Theta0(eta)^2+12*(Tp-1)^2*Theta0(eta))/(3*a3*Pr)]:
> 


(LB,UB):= (0,1):


BCs:= [
  
  U0(0) = 0, U1(0) = 0, N0(0) = 0, N1(0) = 0, Theta0(0) = 0, Theta1(0) = 0, U0(1) = 0, U1(1) = 0, N0(1) = 0, N1(1) = 0, Theta0(1) = 1, Theta1(1) = 0
]:
> 

NULL
> 


Params:= Record(
   
   M1=  1.2, Rd=0.8,la=0.8,n1=1.2,Q=0.2,Pj=0.001,Ra=0.8,Ec=1,    Pr= 21,   delta= 0.2,    t1= (1/4)*Pi, lambda0=2,lambda1=3,   Qc= 0.1,    l1= 1,K=0.4,H=3 ,deltat=0.05  ):
   
> 

NBVs:= [   
 
a1**D(U0)(0) = `C*__f` , # Skin friction coefficient
 (a4+(4*Rd*(1/3))*(1+(Tp-1)*(Theta0(0)+0.1e-2*exp(l1*t1)*Theta1(0)))^3)*((D(Theta0))(0)+0.1e-2*exp(l1*t1)*(D(Theta1))(0)) = `Nu*`    # Nusselt number     
]:
Nu:= `Nu*`:
Cf:= `C*__f`:

 
> 

Solve:= module()
local
   nbvs_rhs:= rhs~(:-NBVs), #just the names
   Sol, #numeric dsolve BVP solution of any 'output' form
   ModuleApply:= subs(
      _Sys= {:-ODEs[], :-BCs[], :-NBVs[]},
      proc({
          M1::realcons:=  Params:-M1,
         Pr::realcons:= Params:-Pr,
         Rd::realcons:= Params:-Rd,
         la::realcons:= Params:-la,
         Tp::realcons:= Params:-Tp,
         n1::realcons:= Params:-n1,
         Q::realcons:= Params:-Q,
         Pj::realcons:= Params:-Pj,
         Ra::realcons:= Params:-Ra,
         Ec::realcons:= Params:-Ec,
         t1::realcons:=  Params:-t1,
         delta::realcons:= Params:-delta,
         lambda0::realcons:= Params:-lambda0,
         lambda1::realcons:= Params:-lambda1,
         Qc::realcons:= Params:-Qc,
         K::realcons:= Params:-K,
         l1::realcons:= Params:-l1,
         H::realcons:= Params:-H
      })
         Sol:= dsolve(_Sys, _rest, numeric);
         AccumData(Sol, {_options});
         Sol
      end proc
   ),
   AccumData:= proc(
      Sol::{Matrix, procedure, list({name, function}= procedure)},
      params::set(name= realcons)
   )
   local n, nbvs;
      if Sol::Matrix then
         nbvs:= seq(n = Sol[2,1][1,Pos(n)], n= nbvs_rhs)
      else
         nbvs:= (nbvs_rhs =~ eval(nbvs_rhs, Sol(:-LB)))[]
      fi;
      SavedData[params]:= Record[packed](params[], nbvs)
   end proc,
   ModuleLoad:= eval(Init);
export
   SavedData, #table of Records
   Pos, #Matrix column indices of nbvs
   Init:= proc()
      Pos:= proc(n::name) option remember; local p; member(n, Sol[1,1], 'p'); p end proc;
      SavedData:= table();
      return
   end proc ;
   ModuleLoad()
end module:
 
> 


 
> 

 

> 

#procedure that generates 3-D plots (dropped-shadow contour + surface) of an expression


ParamPlot3d:= proc(
   Z::{procedure, `module`}, #procedure that extracts z-value from Solve's dsolve solution
   X::name= range(realcons), #x-axis-parameter range
   Y::name= range(realcons), #y-axis-parameter range
   FP::list(name= realcons), #fixed values of other parameters
   {
      #fraction of empty space above and below plot (larger "below"
      #value improves view of dropped-shadow contourplot):
      zmargin::[realcons,realcons]:= [.05,0.15],
      eta::realcons:= :-LB, #independent variable value
      dsolveopts::list({name, name= anything}):= [],
      contouropts::list({name, name= anything}):= [],
      surfaceopts::list({name, name= anything}):=[]    
   }
)
local
   LX:= lhs(X), RX:= rhs(X), LY:= lhs(Y), RY:= rhs(Y),
   Zremember:= proc(x,y)
   option remember; #Used because 'grid' should be the same for both plots.
      Z(
         Solve(
            LX= x, LY= y, FP[],
            #Default dsolve options can be changed by setting 'dsolveopts':
            'abserr'= 0.5e-7, 'interpolant'= false, 'output'= Array([eta]),  
            dsolveopts[]
         )
      )
   end proc,
   plotspec:= (Zremember, RX, RY),
   C:= plots:-contourplot(
      plotspec,
      #These default plot options can be changed by setting 'contouropts':
      'grid'= [25,25], 'contours'= 5, 'filled',
      'coloring'= ['yellow', 'orange'], 'color'= 'green',
      contouropts[]
   ),
   P:= plot3d(
      plotspec,
      #These default plot options can be changed by setting 'surfaceopts':
      'grid'= [25,25], 'style'= 'surfacecontour', 'contours'= 6,
      surfaceopts[]
   ),
   U, L #z-axis endpoints after margin adjustment
;
   #Stretch z-axis to include margins:
   (U,L):= ((Um,Lm,M,m)-> (M*(Lm-1)+m*Um, M*Lm+m*(Um-1)) /~ (Um+Lm-1))(
      zmargin[],
      (max,min)(op(3, indets(P, 'specfunc'('GRID'))[])) #actual z-axis range
   );
   plots:-display(
      [
         plots:-spacecurve(
            {
               [[lhs(RX),rhs(RY),U],[rhs(RX),rhs(RY),U],[rhs(RX),rhs(RY),L]], #yz backwall
               [[rhs(RX),rhs(RY),U],[rhs(RX),lhs(RY),U],[rhs(RX),lhs(RY),L]]  #xz backwall
            },
            'color'= 'grey', 'thickness'= 0
         ),
         plottools:-transform((x,y)-> [x,y,L])(C), #dropped-shadow contours
         P
      ],
      #These default plot options can be changed simply by putting the option in the
      #ParamPlot3d call:
      'view'= ['DEFAULT', 'DEFAULT', L..U], 'orientation'= [-135, 75], 'axes'= 'frame',
      'labels'= [lhs(X), lhs(Y), Z], 'labelfont'= ['TIMES', 'BOLDOBLIQUE', 16],
      'caption'= nprintf(cat("%a = %4.2f, "$nops(FP)-1, "%a = %4.2f"), (lhs,rhs)~(FP)[]),
      'captionfont'= ['TIMES', 14],
      'projection'= 2/3,   
      _rest
   )
end proc:

> 

NULL
> 

NULL
> 

GetNu := proc (Sol::Matrix) options operator, arrow; Sol[2, 1][1, Solve:-Pos(:-Nu)] end proc
> 

ParamPlot3d(
   GetNu,Q= 0..5, Rd= 0..5, [
   
   Pr= 21   ],
   labels= [Q, gamma, Nu]
);

Error, (in plot/iplot2d/levelcurve) could not evaluate expression

  

``

Download P6_3D_plots.mw

How do I plot binned data in Maple?...

Asked by: Traruh Synred 55
histogram plotting statistics
September 15 2023
0  6

I have data that I've binned in list. I'd like to plot in as a histogram. 

dataplot sort of does it but doesn't give the x-axis that I used but just the bins.

Yes, I know about Histogram from Statistics. To plot 1000000 values I have to enter them all into a list which seems crazy when all I want is a 100 bin histogram. Doing the binning is trivial, but I can't figure out how to plot it with a sensible x-axis (show range used to define the 'histogram')

Nothing works after updating from Maple 2015 to 20...

Asked by: leouam 25
installation incomplete-question
September 15 2023
0  3

Hello,

I am experiencing difficulties using my old Maple programs with the newer version. I tried changing the types of inputs and the typesetting level, but it just doesn't work. I would appreciate it if someone could help me overcome my ignorance.

Some simple input is attached with the output.

how to input complex function in a complex differe...

Asked by: bashar27 55
August 20 2023
0  0

restart;
alias(u = u(x, y, t), f = f(x, y, t));
                              u, f
u := (f+sqrt(R))*exp(I*R*t);
                    /     (1/2)\           
                    \f + R     / exp(I R t)
pde1 := I*(diff(u, t))+diff(u, x, x)+2*lambda*u*abs(u)*abs(u)-gamma*(diff(u, x, t));
   // d   \                /     (1/2)\             \
 I ||--- f| exp(I R t) + I \f + R     / R exp(I R t)|
   \\ dt  /                                         /

      / d  / d   \\           
    + |--- |--- f|| exp(I R t)
      \ dx \ dx  //           

               /     (1/2)\                           2 
    + 2 lambda \f + R     / exp(I R t) (exp(-Im(R t)))  

               2
   |     (1/2)| 
   |f + R     | 

            // d  / d   \\                / d   \             \
    - gamma ||--- |--- f|| exp(I R t) + I |--- f| R exp(I R t)|
            \\ dx \ dt  //                \ dx  /             /
 

      

DTM method with Dsolve method comparision...

Asked by: SHIVAS 35
ode homework dsolve
August 18 2023
0  0

how to plot graphs for both methods and comparison of different method values for Diff(f(eta),eta, eta) at eta =0

 

> 

NULL
> 

NULL
> 

restart
> 

F[0] := al
> 

F[1] := a2
> 

F[2] := a3
> 

F[3] := a4
> 

G[0] := a5
> 

G[1] := a6
> 

T[0] := a7
> 

T[1] := a8
> 

Q[0] := a9
> 

Q[1] := a10
> 

n[1] := 1
> 

for k from 0 to n[1] do F[k+4] := solve((1+a)*(k+1)*(k+2)*(k+3)*(k+4)*F[k+4]-a*(k+1)*(k+2)*G[k+2]-R*(sum(F[k-m]*(m+1)*(m+2)*(m+3)*F[m+3], m = 0 .. k))+R*(sum((k-m+1)*F[k-m+1]*(m+1)*(m+2)*F[m+2], m = 0 .. k)), F[k+4]) end do

-(1/12)*(R*a2*a3-3*R*a4*al-a*G[2])/(1+a)

  

-(1/60)*(R^2*a2*a3*al-3*R^2*a4*al^2+2*R*a*a3^2-R*a*al*G[2]+2*R*a3^2-3*a^2*G[3]-3*a*G[3])/(1+a)^2

 (1)
> 

n[2] := 3
> 

for k from 0 to n[2] do G[k+2] := solve(b*(k+1)*(k+2)*G[k+2]+a*(k+1)*(k+2)*F[k+2]-2*a*G[k]-c*R*(sum((m+1)*G[m+1]*F[k-m], m = 0 .. k))+c*R*(sum(G[k-m]*(m+1)*F[m+1], m = 0 .. k)), G[k+2]) end do

-(1/2)*(R*a2*a5*c-R*a6*al*c+2*a*a3-2*a*a5)/b

  

-(1/6)*(R^2*a2*a5*al*c^2-R^2*a6*al^2*c^2+2*R*a*a3*al*c-2*R*a*a5*al*c+2*R*a3*a5*b*c+6*a*a4*b-2*a*a6*b)/b^2

  

-(1/24)*(R^3*a*a2*a5*al^2*c^3-R^3*a*a6*al^3*c^3+R^3*a2*a5*al^2*c^3-R^3*a6*al^3*c^3+2*R^2*a^2*a3*al^2*c^2-2*R^2*a^2*a5*al^2*c^2+R^2*a*a2^2*a5*b*c^2-R^2*a*a2*a6*al*b*c^2+2*R^2*a*a3*a5*al*b*c^2+2*R^2*a*a3*al^2*c^2-2*R^2*a*a5*al^2*c^2+R^2*a2^2*a5*b*c^2-R^2*a2*a6*al*b*c^2+2*R^2*a3*a5*al*b*c^2+2*R*a^2*a2*a3*b*c-R*a^2*a2*a5*b*c+6*R*a^2*a4*al*b*c-3*R*a^2*a6*al*b*c+2*R*a*a3*a6*b^2*c+6*R*a*a4*a5*b^2*c-2*R*a*a2*a3*b^2+2*R*a*a2*a3*b*c+6*R*a*a4*al*b^2+6*R*a*a4*al*b*c-4*R*a*a6*al*b*c+2*R*a3*a6*b^2*c+6*R*a4*a5*b^2*c+2*a^3*a3*b-2*a^3*a5*b+4*a^2*a3*b-4*a^2*a5*b)/(b^3*(1+a))

  

-(1/120)*(R^4*a^2*a2*a5*al^3*c^4-R^4*a^2*a6*al^4*c^4+2*R^4*a*a2*a5*al^3*c^4-2*R^4*a*a6*al^4*c^4+R^4*a2*a5*al^3*c^4-R^4*a6*al^4*c^4+2*R^3*a^3*a3*al^3*c^3-2*R^3*a^3*a5*al^3*c^3+3*R^3*a^2*a2^2*a5*al*b*c^3-3*R^3*a^2*a2*a6*al^2*b*c^3+2*R^3*a^2*a3*a5*al^2*b*c^3+4*R^3*a^2*a3*al^3*c^3-4*R^3*a^2*a5*al^3*c^3+6*R^3*a*a2^2*a5*al*b*c^3-6*R^3*a*a2*a6*al^2*b*c^3+4*R^3*a*a3*a5*al^2*b*c^3+2*R^3*a*a3*al^3*c^3-2*R^3*a*a5*al^3*c^3+3*R^3*a2^2*a5*al*b*c^3-3*R^3*a2*a6*al^2*b*c^3+2*R^3*a3*a5*al^2*b*c^3+6*R^2*a^3*a2*a3*al*b*c^2-4*R^2*a^3*a2*a5*al*b*c^2+6*R^2*a^3*a4*al^2*b*c^2-4*R^2*a^3*a6*al^2*b*c^2+4*R^2*a^2*a2*a3*a5*b^2*c^2-R^2*a^2*a2*a5^2*b^2*c^2+2*R^2*a^2*a3*a6*al*b^2*c^2+6*R^2*a^2*a4*a5*al*b^2*c^2+R^2*a^2*a5*a6*al*b^2*c^2-2*R^2*a^2*a2*a3*al*b^2*c+12*R^2*a^2*a2*a3*al*b*c^2-R^2*a^2*a2*a5*al*b^2*c-6*R^2*a^2*a2*a5*al*b*c^2+6*R^2*a^2*a4*al^2*b^2*c+12*R^2*a^2*a4*al^2*b*c^2+R^2*a^2*a6*al^2*b^2*c-10*R^2*a^2*a6*al^2*b*c^2-2*R^2*a*a2*a3*a5*b^3*c+8*R^2*a*a2*a3*a5*b^2*c^2-R^2*a*a2*a5^2*b^2*c^2+4*R^2*a*a3*a6*al*b^2*c^2+6*R^2*a*a4*a5*al*b^3*c+12*R^2*a*a4*a5*al*b^2*c^2+R^2*a*a5*a6*al*b^2*c^2-2*R^2*a*a2*a3*al*b^3-2*R^2*a*a2*a3*al*b^2*c+6*R^2*a*a2*a3*al*b*c^2-2*R^2*a*a2*a5*al*b*c^2+6*R^2*a*a4*al^2*b^3+6*R^2*a*a4*al^2*b^2*c+6*R^2*a*a4*al^2*b*c^2-6*R^2*a*a6*al^2*b*c^2-2*R^2*a2*a3*a5*b^3*c+4*R^2*a2*a3*a5*b^2*c^2+2*R^2*a3*a6*al*b^2*c^2+6*R^2*a4*a5*al*b^3*c+6*R^2*a4*a5*al*b^2*c^2+4*R*a^4*a3*al*b*c-4*R*a^4*a5*al*b*c+12*R*a^3*a2*a4*b^2*c-4*R*a^3*a2*a6*b^2*c+2*R*a^3*a5^2*b^2*c+12*R*a^2*a4*a6*b^3*c-2*R*a^3*a3*al*b^2+12*R*a^3*a3*al*b*c+2*R*a^3*a5*al*b^2-12*R*a^3*a5*al*b*c+24*R*a^2*a2*a4*b^2*c-8*R*a^2*a2*a6*b^2*c-4*R*a^2*a3^2*b^3+4*R*a^2*a3*a5*b^2*c+2*R*a^2*a5^2*b^2*c+24*R*a*a4*a6*b^3*c+8*R*a^2*a3*al*b*c-8*R*a^2*a5*al*b*c+12*R*a*a2*a4*b^2*c-4*R*a*a2*a6*b^2*c-4*R*a*a3^2*b^3+4*R*a*a3*a5*b^2*c+12*R*a4*a6*b^3*c+6*a^4*a4*b^2-2*a^4*a6*b^2+18*a^3*a4*b^2-6*a^3*a6*b^2+12*a^2*a4*b^2-4*a^2*a6*b^2)/(b^4*(1+a)^2)

 (2)
> 

n[3] := 3
> 

for k from 0 to n[3] do T[k+2] := solve((k+1)*(k+2)*T[k+2]+p3*(k+1)*(k+2)*Q[k+2]+p1*(sum((m+1)*F[m+1]*T[k-m], m = 0 .. k))-p1*(sum(F[k-m]*(m+1)*T[m+1], m = 0 .. k)), T[k+2]) end do

-(1/2)*p1*a2*a7+(1/2)*p1*al*a8-p3*Q[2]

  

-(1/6)*a2*a7*al*p1^2+(1/6)*a8*al^2*p1^2-(1/3)*al*p1*p3*Q[2]-(1/3)*a3*a7*p1-p3*Q[3]

  

-p3*Q[4]-(1/24)*p1^2*a2^2*a7+(1/24)*a2*p1^2*al*a8-(1/12)*p1*a2*p3*Q[2]-(1/12)*p1*a3*a8-(1/4)*p1*a4*a7-(1/24)*a2*a7*al^2*p1^3+(1/24)*a8*al^3*p1^3-(1/12)*al^2*p1^2*p3*Q[2]-(1/12)*al*a3*a7*p1^2-(1/4)*p1*al*p3*Q[3]

  

(1/120)*(-a*a2*a7*al^3*b*p1^4+a*a8*al^4*b*p1^4-2*a*al^3*b*p1^3*p3*Q[2]-a2*a7*al^3*b*p1^4+a8*al^4*b*p1^4-3*a*a2^2*a7*al*b*p1^3+3*a*a2*a8*al^2*b*p1^3-2*a*a3*a7*al^2*b*p1^3-2*al^3*b*p1^3*p3*Q[2]-6*a*a2*al*b*p1^2*p3*Q[2]-6*a*al^2*b*p1^2*p3*Q[3]-3*a2^2*a7*al*b*p1^3+3*a2*a8*al^2*b*p1^3-2*a3*a7*al^2*b*p1^3+R*a*a2*a5*a7*c*p1-R*a*a6*a7*al*c*p1-4*a*a2*a3*a7*b*p1^2-2*a*a3*a8*al*b*p1^2-6*a*a4*a7*al*b*p1^2-6*a2*al*b*p1^2*p3*Q[2]-6*al^2*b*p1^2*p3*Q[3]+2*R*a2*a3*a7*b*p1-6*R*a4*a7*al*b*p1-12*a*a2*b*p1*p3*Q[3]-24*a*al*b*p1*p3*Q[4]-4*a2*a3*a7*b*p1^2-2*a3*a8*al*b*p1^2-6*a4*a7*al*b*p1^2+2*a^2*a3*a7*p1-2*a^2*a5*a7*p1-12*a*a4*a8*b*p1-12*a2*b*p1*p3*Q[3]-24*al*b*p1*p3*Q[4]-120*a*b*p3*Q[5]-12*a4*a8*b*p1-120*b*p3*Q[5])/(b*(1+a))

 (3)
> 

n[4] := 3
> 

for k from 0 to n[4] do Q[k+2] := solve((k+1)*(k+2)*Q[k+2]+p4*(k+1)*(k+2)*Q[k+2]+p2*(sum((m+1)*F[m+1]*Q[k-m], m = 0 .. k))-p2*(sum(F[k-m]*(m+1)*Q[m+1], m = 0 .. k)), Q[k+2]) end do

(1/2)*p2*(a10*al-a2*a9)/(p4+1)

  

(1/6)*p2*(a10*al^2*p2-a2*a9*al*p2-2*a3*a9*p4-2*a3*a9)/(p4+1)^2

  

(1/24)*p2*(a10*al^3*p2^2-a2*a9*al^2*p2^2+a10*a2*al*p2*p4-a2^2*a9*p2*p4-2*a3*a9*al*p2*p4+a10*a2*al*p2-2*a10*a3*p4^2-a2^2*a9*p2-2*a3*a9*al*p2-6*a4*a9*p4^2-4*a10*a3*p4-12*a4*a9*p4-2*a10*a3-6*a4*a9)/(p4+1)^3

  

(1/120)*p2*(a*a10*al^4*b*p2^3-a*a2*a9*al^3*b*p2^3+R*a*a2*a5*a9*c*p4^3-R*a*a6*a9*al*c*p4^3+3*a*a10*a2*al^2*b*p2^2*p4-3*a*a2^2*a9*al*b*p2^2*p4-2*a*a3*a9*al^2*b*p2^2*p4+a10*al^4*b*p2^3-a2*a9*al^3*b*p2^3+3*R*a*a2*a5*a9*c*p4^2-3*R*a*a6*a9*al*c*p4^2+2*R*a2*a3*a9*b*p4^3-6*R*a4*a9*al*b*p4^3+3*a*a10*a2*al^2*b*p2^2-2*a*a10*a3*al*b*p2*p4^2-3*a*a2^2*a9*al*b*p2^2-4*a*a2*a3*a9*b*p2*p4^2-2*a*a3*a9*al^2*b*p2^2-6*a*a4*a9*al*b*p2*p4^2+3*a10*a2*al^2*b*p2^2*p4-3*a2^2*a9*al*b*p2^2*p4-2*a3*a9*al^2*b*p2^2*p4+3*R*a*a2*a5*a9*c*p4-3*R*a*a6*a9*al*c*p4+6*R*a2*a3*a9*b*p4^2-18*R*a4*a9*al*b*p4^2+2*a^2*a3*a9*p4^3-2*a^2*a5*a9*p4^3-4*a*a10*a3*al*b*p2*p4-12*a*a10*a4*b*p4^3-8*a*a2*a3*a9*b*p2*p4-12*a*a4*a9*al*b*p2*p4+3*a10*a2*al^2*b*p2^2-2*a10*a3*al*b*p2*p4^2-3*a2^2*a9*al*b*p2^2-4*a2*a3*a9*b*p2*p4^2-2*a3*a9*al^2*b*p2^2-6*a4*a9*al*b*p2*p4^2+R*a*a2*a5*a9*c-R*a*a6*a9*al*c+6*R*a2*a3*a9*b*p4-18*R*a4*a9*al*b*p4+6*a^2*a3*a9*p4^2-6*a^2*a5*a9*p4^2-2*a*a10*a3*al*b*p2-36*a*a10*a4*b*p4^2-4*a*a2*a3*a9*b*p2-6*a*a4*a9*al*b*p2-4*a10*a3*al*b*p2*p4-12*a10*a4*b*p4^3-8*a2*a3*a9*b*p2*p4-12*a4*a9*al*b*p2*p4+2*R*a2*a3*a9*b-6*R*a4*a9*al*b+6*a^2*a3*a9*p4-6*a^2*a5*a9*p4-36*a*a10*a4*b*p4-2*a10*a3*al*b*p2-36*a10*a4*b*p4^2-4*a2*a3*a9*b*p2-6*a4*a9*al*b*p2+2*a^2*a3*a9-2*a^2*a5*a9-12*a*a10*a4*b-36*a10*a4*b*p4-12*a10*a4*b)/((p4+1)^4*b*(1+a))

 (4)
> 

U[1] := sum(F[r]*t^r, r = 0 .. n[1]+4)
> 

p[1] := subs(R = 1, a = 1, b = 1, c = 1, p1 = 1, p2 = .8, p3 = .1, p4 = .1, U[1])
> 

U[2] := sum(G[r]*t^r, r = 0 .. n[2]+2)
> 

p[2] := subs(R = 1, a = 1, b = 1, c = 1, p1 = 1, p2 = .8, p3 = .1, p4 = .1, U[2])
> 

U[3] := sum(T[r]*t^r, r = 0 .. n[2]+2)
> 

p[3] := subs(R = 1, a = 1, b = 1, c = 1, p1 = 1, p2 = .8, p3 = .1, p4 = .1, U[3])
> 

U[4] := sum(Q[r]*t^r, r = 0 .. n[2]+2)
> 

p[4] := subs(R = 1, a = 1, b = 1, c = 1, p1 = 1, p2 = .8, p3 = .1, p4 = .1, U[4])
> 

e1 := subs(t = -1, p[1]) = 0
> 

e2 := subs(t = -1, diff(p[1], t)) = 0
> 

e3 := subs(t = 1, diff(p[1], t)) = -1
> 

e4 := subs(t = 1, p[1]) = 0
> 

e5 := subs(t = -1, p[2]) = 0
> 

e6 := subs(t = 1, p[2]) = 1
> 

e7 := subs(t = -1, p[3]) = 1
> 

e8 := subs(t = 1, p[3]) = 0
> 

e9 := subs(t = -1, p[4]) = 1
> 

e10 := subs(t = 1, p[4]) = 0
> 

j := {e1, e10, e2, e3, e4, e5, e6, e7, e8, e9}
> 

j := solve(j)
> 

sj := evalf(j)

{a10 = -3.476623407, a2 = -5.754056209, a3 = .1776219452, a4 = 11.75811242, a5 = 1.324264301, a6 = -684.5523526, a7 = -.2700369914, a8 = 1.152227714, a9 = 2.191204245, al = 0.3618902741e-1}, {a10 = -.5218741555, a2 = .2575353882, a3 = -.2672619833, a4 = -.2650707765, a5 = 0.7065354871e-1, a6 = .1172581545, a7 = .6100817436, a8 = -.5277387253, a9 = .5842364534, al = .2586309916}, {a10 = -4.849411034, a2 = 11.61910224, a3 = -20.01600142, a4 = -22.98820448, a5 = -303.7401922, a6 = -153.4446663, a7 = -7.896832028, a8 = -4.917031955, a9 = -9.645684059, al = 10.13300071}, {a10 = -12.41434918+6.055636678*I, a2 = -6.912869603-3.362489448*I, a3 = -9.364948739-.7062944755*I, a4 = 14.07573921+6.724978896*I, a5 = -106.6284397-3.087774395*I, a6 = 184.4202683+38.56644530*I, a7 = 2.689687372-4.048821750*I, a8 = -4.715343127+5.167588829*I, a9 = 8.474095612-5.785653488*I, al = 4.807474369+.3531472377*I}, {a10 = -8.462156658-37.78952093*I, a2 = -22.10322629+.7748996783*I, a3 = -2.926063539-87.71943544*I, a4 = 44.45645258-1.549799357*I, a5 = 126.1645842+1357.517358*I, a6 = -880.5344239+73.01362458*I, a7 = -96.56841781+19.40514883*I, a8 = -11.30265439-58.49348719*I, a9 = -59.25678527+13.86225901*I, al = 1.588031769+43.85971772*I}, {a10 = 21.28781597+0.9115942334e-2*I, a2 = -2.190767380-.1297694199*I, a3 = 0.4834062985e-1-8.617807139*I, a4 = 4.631534761+.2595388398*I, a5 = -1.070222696-4.103740084*I, a6 = 28.93315819+1.060309794*I, a7 = -.6440073083+2.959900705*I, a8 = 3.178056838-1.712994921*I, a9 = -1.124006374+8.865509135*I, al = .1008296851+4.308903570*I}, {a10 = -2.226772562-4.893664011*I, a2 = -5.213384606-.4953312060*I, a3 = 1.881656676-24.64377975*I, a4 = 10.67676921+.9906624121*I, a5 = -5.922885277-14.38776520*I, a6 = 9.281006594-6.268746147*I, a7 = -8.563253672+2.519226454*I, a8 = -2.293245547-7.112743663*I, a9 = -4.948019289+2.035858706*I, al = -.8158283379+12.32188987*I}, {a10 = -3.311080211+1.380948844*I, a2 = -6.825505968+3.517539795*I, a3 = 10.11566715-.6387142267*I, a4 = 13.90101194-7.035079589*I, a5 = 106.6696011-4.144959139*I, a6 = 183.4179274-43.03852019*I, a7 = -1.117431335-0.4722817327e-1*I, a8 = -1.705921790+.2164542338*I, a9 = -2.431505210+.6185873236*I, al = -4.932833576+.3193571133*I}, {a10 = 1.720689325, a2 = 11.30494181, a3 = 20.89441402, a4 = -22.35988362, a5 = 304.5741226, a6 = -141.0519632, a7 = -3.607319024, a8 = 2.107261122, a9 = -3.764007990, al = -10.32220701}, {a10 = -3.311080211-1.380948844*I, a2 = -6.825505968-3.517539795*I, a3 = 10.11566715+.6387142267*I, a4 = 13.90101194+7.035079589*I, a5 = 106.6696011+4.144959139*I, a6 = 183.4179274+43.03852019*I, a7 = -1.117431335+0.4722817327e-1*I, a8 = -1.705921790-.2164542338*I, a9 = -2.431505210-.6185873236*I, al = -4.932833576-.3193571133*I}, {a10 = -2.226772562+4.893664011*I, a2 = -5.213384606+.4953312060*I, a3 = 1.881656676+24.64377975*I, a4 = 10.67676921-.9906624121*I, a5 = -5.922885277+14.38776520*I, a6 = 9.281006594+6.268746147*I, a7 = -8.563253672-2.519226454*I, a8 = -2.293245547+7.112743663*I, a9 = -4.948019289-2.035858706*I, al = -.8158283379-12.32188987*I}, {a10 = 21.28781597-0.9115942334e-2*I, a2 = -2.190767380+.1297694199*I, a3 = 0.4834062985e-1+8.617807139*I, a4 = 4.631534761-.2595388398*I, a5 = -1.070222696+4.103740084*I, a6 = 28.93315819-1.060309794*I, a7 = -.6440073083-2.959900705*I, a8 = 3.178056838+1.712994921*I, a9 = -1.124006374-8.865509135*I, al = .1008296851-4.308903570*I}, {a10 = -8.462156658+37.78952093*I, a2 = -22.10322629-.7748996783*I, a3 = -2.926063539+87.71943544*I, a4 = 44.45645258+1.549799357*I, a5 = 126.1645842-1357.517358*I, a6 = -880.5344239-73.01362458*I, a7 = -96.56841781-19.40514883*I, a8 = -11.30265439+58.49348719*I, a9 = -59.25678527-13.86225901*I, al = 1.588031769-43.85971772*I}, {a10 = -12.41434918-6.055636678*I, a2 = -6.912869603+3.362489448*I, a3 = -9.364948739+.7062944755*I, a4 = 14.07573921-6.724978896*I, a5 = -106.6284397+3.087774395*I, a6 = 184.4202683-38.56644530*I, a7 = 2.689687372+4.048821750*I, a8 = -4.715343127-5.167588829*I, a9 = 8.474095612+5.785653488*I, al = 4.807474369-.3531472377*I}

 (5)
> 

p[1] := subs(a10 = -.5218741555, a2 = .2575353882, a3 = -.2672619833, a4 = -.2650707765, a5 = 0.7065354871e-1, a6 = .1172581545, a7 = .6100817436, a8 = -.5277387253, a9 = .5842364534, al = .2586309916, p[1])

.2586309916+.2575353882*t-.2672619833*t^2-.2650707765*t^3+0.8630991633e-2*t^4+0.7535388242e-2*t^5

 (6)
> 

p[2] := subs(a10 = -.5218741555, a2 = .2575353882, a3 = -.2672619833, a4 = -.2650707765, a5 = 0.7065354871e-1, a6 = .1172581545, a7 = .6100817436, a8 = -.5277387253, a9 = .5842364534, al = .2586309916, p[2])

0.7065354871e-1+.1172581545*t+.3439809338*t^2+.3401058738*t^3+0.8536551748e-1*t^4+0.4263597162e-1*t^5

 (7)
> 

p[3] := subs(a10 = -.5218741555, a2 = .2575353882, a3 = -.2672619833, a4 = -.2650707765, a5 = 0.7065354871e-1, a6 = .1172581545, a7 = .6100817436, a8 = -.5277387253, a9 = .5842364534, al = .2586309916, p[3])

.6100817436-.5277387253*t-.1364241818*t^2+0.3945483872e-1*t^3+0.2634243820e-1*t^4-0.1171611337e-1*t^5

 (8)
> 

p[4] := subs(a10 = -.5218741555, a2 = .2575353882, a3 = -.2672619833, a4 = -.2650707765, a5 = 0.7065354871e-1, a6 = .1172581545, a7 = .6100817436, a8 = -.5277387253, a9 = .5842364534, al = .2586309916, p[4])

.5842364534-.5218741555*t-.1037943244*t^2+0.3134539737e-1*t^3+0.1955787096e-1*t^4-0.9471241840e-2*t^5

 (9)
> 

NULL
> 

value*of*D@@2*F(0)*For*R = 1, 1.5, `and`(2*Using*Both*DTM*scheme, dsolve*method)
> 

 

Download DTM_practice.mw

Questions on Visualization Methods...

Asked by: jganding 135
plotting color
August 09 2023
0  0

I'm attempting to visualize temperature averages across a 2 dimentional space (e.g., a square plate) with fixed heat sources. The 3rd dimension (z axis) represents temperature.  I have created several visualizations but have questions about how these plots work.  The model is attached and the questions will make sense once you open the worksheet.

  1. Using the "colorscheme" option on a couple of matrixplots, I get the error "[Length of output exceeds limit of 1000000]" and the plot doesn't show.  However using the "display()" command on those same plots does render the plot.  Is there a way around this error (i.e., rendering the plot directly) or should I just suppress the error using a colon at the end of the plot statement and rely on display() to show the plot?
  2. I've created a heat map as one of the visualizations.  Is there a way to access the color values at each of the "cells" of the heat map? I would like to use these colors elsewhere in the model but I'm not sure if there is a way to access the color values.
  3. Using a 3D point plot as one of the visualization options, I use the colorschemes with options "xgradient", "ygradient", and "zgradient".  For some reason, "xgradient" and "ygradient" work as expected but "zgradient" looks the same as "ygradient".  How do I get the color transition to change along the z axis rather than only x and y axes?

Thank you for your help on these questions.

temperature_profile_(experimental)(v01).mw

linearize the complex conjugate function partial d...

Asked by: bashar27 55
linearize differential-equations conjugate
July 20 2023
0  0

restart;
alias(u = u(x, z, t), f = f(x, z, t));
                              u, f
u := (f+sqrt(R))*exp(I*R*x);
                    /     (1/2)\           
                    \f + R     / exp(I R x)
pde1 := I*(diff(u, z))+diff(u, x, x)+diff(u, t, t)+u*abs(u)*abs(u)-(u*abs(u)*abs(u))*abs(u)*abs(u);
    / d   \              / d  / d   \\           
  I |--- f| exp(I R x) + |--- |--- f|| exp(I R x)
    \ dz  /              \ dx \ dx  //           

           / d   \                /     (1/2)\  2           
     + 2 I |--- f| R exp(I R x) - \f + R     / R  exp(I R x)
           \ dx  /                                          

       / d  / d   \\           
     + |--- |--- f|| exp(I R x)
       \ dt \ dt  //           

                                                            2
       /     (1/2)\                           2 |     (1/2)| 
     + \f + R     / exp(I R x) (exp(-Im(R x)))  |f + R     | 

                                                            4
       /     (1/2)\                           4 |     (1/2)| 
     - \f + R     / exp(I R x) (exp(-Im(R x)))  |f + R     | 

simplify(%);
         / d   \              / d  / d   \\           
       I |--- f| exp(I R x) + |--- |--- f|| exp(I R x)
         \ dz  /              \ dx \ dx  //           

                / d   \                 2             
          + 2 I |--- f| R exp(I R x) - R  exp(I R x) f
                \ dx  /                               

             (5/2)              / d  / d   \\           
          - R      exp(I R x) + |--- |--- f|| exp(I R x)
                                \ dt \ dt  //           

                                               2  
                                   |     (1/2)|   
          + exp(I R x - 2 Im(R x)) |f + R     |  f

                                               2       
                                   |     (1/2)|   (1/2)
          + exp(I R x - 2 Im(R x)) |f + R     |  R     

                                               4  
                                   |     (1/2)|   
          - exp(I R x - 4 Im(R x)) |f + R     |  f

                                               4       
                                   |     (1/2)|   (1/2)
          - exp(I R x - 4 Im(R x)) |f + R     |  R     
collect(%, exp(I*R*x));
  /  (5/2)       / d   \      2       / d   \   / d  / d   \\
  |-R      + 2 I |--- f| R - R  f + I |--- f| + |--- |--- f||
  \              \ dx  /              \ dz  /   \ dx \ dx  //

       / d  / d   \\\           
     + |--- |--- f||| exp(I R x)
       \ dt \ dt  ///           

                                          2  
                              |     (1/2)|   
     + exp(I R x - 2 Im(R x)) |f + R     |  f

                                          2       
                              |     (1/2)|   (1/2)
     + exp(I R x - 2 Im(R x)) |f + R     |  R     

                                          4  
                              |     (1/2)|   
     - exp(I R x - 4 Im(R x)) |f + R     |  f

                                          4       
                              |     (1/2)|   (1/2)
     - exp(I R x - 4 Im(R x)) |f + R     |  R     
 

Bifurcation Diagram from my system of equations...

Asked by: Elisha 35
ode differential-equations bifurcation
July 08 2023
0  0

Please help with the bifurcation diagram for the system and parameter values below

> 

NULL

with(VectorCalculus)

[`&x`, `*`, `+`, `-`, `.`, `<,>`, `<|>`, About, AddCoordinates, ArcLength, BasisFormat, Binormal, ConvertVector, CrossProduct, Curl, Curvature, D, Del, DirectionalDiff, Divergence, DotProduct, Flux, GetCoordinateParameters, GetCoordinates, GetNames, GetPVDescription, GetRootPoint, GetSpace, Gradient, Hessian, IsPositionVector, IsRootedVector, IsVectorField, Jacobian, Laplacian, LineInt, MapToBasis, Nabla, Norm, Normalize, PathInt, PlotPositionVector, PlotVector, PositionVector, PrincipalNormal, RadiusOfCurvature, RootedVector, ScalarPotential, SetCoordinateParameters, SetCoordinates, SpaceCurve, SurfaceInt, TNBFrame, TangentLine, TangentPlane, TangentVector, Torsion, Vector, VectorField, VectorPotential, VectorSpace, Wronskian, diff, eval, evalVF, int, limit, series]

 (1)
> 

interface(imaginaryunit = F)

I

 (2)

M := Pi*theta-S*c__1-S*lambda+S__v*v__2

Pi*theta-S*c__1-S*lambda+S__v*v__2

 (3)

Y := -S__v*c__2*lambda+Pi*b__1+S*v__1-S__v*c__3

-S__v*c__2*lambda+Pi*b__1+S*v__1-S__v*c__3

 (4)

P := S__v*alpha+`&rho;__A`*A+c__4*`&rho;__Q`*Q+I*`&rho;__I`-µ*V

Q*c__4*rho__Q+A*rho__A+I*rho__I+S__v*alpha-V*µ

 (5)

R := S__v*c__2*lambda-E*c__5+S*lambda

S__v*c__2*lambda-E*c__5+S*lambda

 (6)

U := E*a*delta+Q*k*`&rho;__Q`-A*c__6

E*a*delta+Q*k*rho__Q-A*c__6

 (7)

L := c__7*E-I*c__8

E*c__7-I*c__8

 (8)

X := q__E*E+I*q__I-c__9*Q

E*q__E+I*q__I-Q*c__9

 (9)

solve({L = 0, M = 0, P = 0, R = 0, U = 0, X = 0, Y = 0}, {I, A, E, Q, S, S__v, V})

{A = (a*c__8*c__9*delta+c__7*k*q__I*rho__Q+c__8*k*q__E*rho__Q)*lambda*Pi*(b__1*c__1*c__2+b__1*c__2*lambda+c__2*lambda*theta+c__2*theta*v__1+b__1*v__2+c__3*theta)/(c__6*c__9*c__5*c__8*(c__1*c__2*lambda+c__2*lambda^2+c__1*c__3+c__3*lambda-v__1*v__2)), E = lambda*Pi*(b__1*c__1*c__2+b__1*c__2*lambda+c__2*lambda*theta+c__2*theta*v__1+b__1*v__2+c__3*theta)/(c__5*(c__1*c__2*lambda+c__2*lambda^2+c__1*c__3+c__3*lambda-v__1*v__2)), I = c__7*lambda*Pi*(b__1*c__1*c__2+b__1*c__2*lambda+c__2*lambda*theta+c__2*theta*v__1+b__1*v__2+c__3*theta)/(c__5*c__8*(c__1*c__2*lambda+c__2*lambda^2+c__1*c__3+c__3*lambda-v__1*v__2)), Q = (c__7*q__I+c__8*q__E)*lambda*Pi*(b__1*c__1*c__2+b__1*c__2*lambda+c__2*lambda*theta+c__2*theta*v__1+b__1*v__2+c__3*theta)/(c__9*c__5*c__8*(c__1*c__2*lambda+c__2*lambda^2+c__1*c__3+c__3*lambda-v__1*v__2)), S = Pi*(c__2*lambda*theta+b__1*v__2+c__3*theta)/(c__1*c__2*lambda+c__2*lambda^2+c__1*c__3+c__3*lambda-v__1*v__2), S__v = Pi*(b__1*c__1+b__1*lambda+theta*v__1)/(c__1*c__2*lambda+c__2*lambda^2+c__1*c__3+c__3*lambda-v__1*v__2), V = Pi*(a*b__1*c__1*c__2*c__8*c__9*delta*lambda*rho__A+a*b__1*c__2*c__8*c__9*delta*lambda^2*rho__A+a*c__2*c__8*c__9*delta*lambda^2*rho__A*theta+a*c__2*c__8*c__9*delta*lambda*rho__A*theta*v__1+b__1*c__1*c__2*c__4*c__6*c__7*lambda*q__I*rho__Q+b__1*c__1*c__2*c__4*c__6*c__8*lambda*q__E*rho__Q+b__1*c__1*c__2*c__7*k*lambda*q__I*rho__A*rho__Q+b__1*c__1*c__2*c__8*k*lambda*q__E*rho__A*rho__Q+b__1*c__2*c__4*c__6*c__7*lambda^2*q__I*rho__Q+b__1*c__2*c__4*c__6*c__8*lambda^2*q__E*rho__Q+b__1*c__2*c__7*k*lambda^2*q__I*rho__A*rho__Q+b__1*c__2*c__8*k*lambda^2*q__E*rho__A*rho__Q+c__2*c__4*c__6*c__7*lambda^2*q__I*rho__Q*theta+c__2*c__4*c__6*c__7*lambda*q__I*rho__Q*theta*v__1+c__2*c__4*c__6*c__8*lambda^2*q__E*rho__Q*theta+c__2*c__4*c__6*c__8*lambda*q__E*rho__Q*theta*v__1+c__2*c__7*k*lambda^2*q__I*rho__A*rho__Q*theta+c__2*c__7*k*lambda*q__I*rho__A*rho__Q*theta*v__1+c__2*c__8*k*lambda^2*q__E*rho__A*rho__Q*theta+c__2*c__8*k*lambda*q__E*rho__A*rho__Q*theta*v__1+a*b__1*c__8*c__9*delta*lambda*rho__A*v__2+a*c__3*c__8*c__9*delta*lambda*rho__A*theta+b__1*c__1*c__2*c__6*c__7*c__9*lambda*rho__I+b__1*c__2*c__6*c__7*c__9*lambda^2*rho__I+b__1*c__4*c__6*c__7*lambda*q__I*rho__Q*v__2+b__1*c__4*c__6*c__8*lambda*q__E*rho__Q*v__2+b__1*c__7*k*lambda*q__I*rho__A*rho__Q*v__2+b__1*c__8*k*lambda*q__E*rho__A*rho__Q*v__2+c__2*c__6*c__7*c__9*lambda^2*rho__I*theta+c__2*c__6*c__7*c__9*lambda*rho__I*theta*v__1+c__3*c__4*c__6*c__7*lambda*q__I*rho__Q*theta+c__3*c__4*c__6*c__8*lambda*q__E*rho__Q*theta+c__3*c__7*k*lambda*q__I*rho__A*rho__Q*theta+c__3*c__8*k*lambda*q__E*rho__A*rho__Q*theta+alpha*b__1*c__1*c__5*c__6*c__8*c__9+alpha*b__1*c__5*c__6*c__8*c__9*lambda+alpha*c__5*c__6*c__8*c__9*theta*v__1+b__1*c__6*c__7*c__9*lambda*rho__I*v__2+c__3*c__6*c__7*c__9*lambda*rho__I*theta)/(c__5*c__6*c__8*c__9*µ*(c__1*c__2*lambda+c__2*lambda^2+c__1*c__3+c__3*lambda-v__1*v__2))}

 (10)
> 

``
> 

lambda := beta*(I+`&eta;__A`*A+`&eta;__Q`*Q)/N

beta*(I+eta__A*A+eta__Q*Q)/N

 (11)
> 

``
> 

NULL
> 

k := .15

.15

 (12)
> 

delta := .125

.125

 (13)
> 

mu := 0.464360344e-4

0.464360344e-4

 (14)
> 

pi := .464360344

.464360344

 (15)
> 

delta__Q := 0.6847e-3

0.6847e-3

 (16)
> 

beta := .1086

.1086

 (17)
> 

q__E := 0.18113e-3

0.18113e-3

 (18)
> 

rho__Q := 0.815e-1

0.815e-1

 (19)
> 

a := .16255

.16255

 (20)
> 

v__1 := 0.5e-1

0.5e-1

 (21)
> 

v__2 := 0.5e-1

0.5e-1

 (22)
> 

alpha := 0.57e-1

0.57e-1

 (23)
> 

lambda := 0.765e-2

0.765e-2

 (24)
> 

rho__A := 0.915e-1

0.915e-1

 (25)
> 

rho__I := 0.515e-1

0.515e-1

 (26)
> 

a := .16255

.16255

 (27)
> 

q__I := 0.1923e-2

0.1923e-2

 (28)
> 

q__A := 0.4013e-7

0.4013e-7

 (29)
> 

eta__A := .1213

.1213

 (30)
> 

eta__Q := 0.3808e-2

0.3808e-2

 (31)
> 

w := .5925

.5925

 (32)

Download Bifurcation_Equation.mw

Impliment of Artificial Neural Network ...

Asked by: KIRAN SAJJAN 40
ode homework dsolve
April 27 2023
1  6

Hello,

Can we impliment Artificial Neural Network for nonlinear coupled ODE equation with boundary conditions.? In maple

I wont seen any post regarding ANN in mapleprime.

I need help to solve ODE using forward-backward sw...

Asked by: Muhammad_Qozeem 5
March 25 2023
1  4

Maple code for solving system of ODE using forward-backward sweep method.

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