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error in dsolve ...

Asked by: KIRAN SAJJAN 40
ode homework dsolve
June 13 2023
0  4

am attaching the worksheet of the problem please help me to solve not able to  compute coupled

error.mw

error in f solve (AGM )...

Asked by: KIRAN SAJJAN 40
rootfinding fsolve numeric
June 02 2023
0  5

 

> 

restart; with(plots)
> 

PDEtools[declare]((F, T, G, H)(Y), prime = Y)

` F`(Y)*`will now be displayed as`*F

  

` T`(Y)*`will now be displayed as`*T

  

` G`(Y)*`will now be displayed as`*G

  

` H`(Y)*`will now be displayed as`*H

  

`derivatives with respect to`*Y*`of functions of one variable will now be displayed with '`

 (1)
> 

p1 := 0.1e-1; p2 := 0.3e-1; p3 := 0.5e-1; p := p1+p2+p3
> 

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

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

sigma2 := 0.210e-5; rs2 := 5700; ks2 := 25; cps2 := 523
> 

sigma3 := 6.30*10^7; rs3 := 10500; ks3 := 429; cps3 := 235
> 

sigma4 := 10^(-10); rs4 := 3970; ks4 := 40; cps4 := 765
> 

sigma5 := 1.69*10^7; rs5 := 7140; ks5 := 116; cps5 := 390
> 

sigma6 := 4.10*10^7; rs6 := 19300; ks6 := 318; cps6 := 129
> 

``
> 

M := 1; S1 := .5; A := 1; delta := 0.1e-2; g := .1; Gr := .5; betu := .5; bett := .5; Pr := 21; Ec := .5; bet := 1; S2 := .5; Rd := 1; Q := .1; Ra := .5; S := .1
> 

alp := .1
> 

``
> 

``
> 

B1 := 1+2.5*p+6.2*p^2; B2 := 1+13.5*p+904.4*p^2; B3 := 1+37.1*p+612.6*p^2; B4 := (ks1+2*kf-2*p*(kf-ks1))/(ks1+2*kf+p*(kf-ks1)); B5 := (ks2+3.9*kf-3.9*p*(kf-ks2))/(ks2+3.9*kf+p*(kf-ks2)); B6 := (ks3+4.7*kf-4.7*p*(kf-ks3))/(ks3+4.7*kf+p*(kf-ks3)); B7 := (ks4+2*kf-2*p*(kf-ks4))/(ks4+2*kf+p*(kf-ks4)); B8 := (ks5+3.9*kf-3.9*p*(kf-ks5))/(ks5+3.9*kf+p*(kf-ks5)); B9 := (ks6+4.7*kf-4.7*p*(kf-ks6))/(ks6+4.7*kf+p*(kf-ks6))
> 

a1 := B1*p1+B2*p2+B3*p3
> 

a2 := 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
> 

``
> 

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
> 

a6 := B1*p1+B2*p2+B3*p3
> 

a7 := 1-p1-p2-p3+p1*rs4/rf+p2*rs5/rf+p3*rs6/rf
> 

a8 := 1-p1-p2-p3+p1*rs4*cps4/(rf*cpf)+p2*rs5*cps5/(rf*cpf)+p3*rs6*cps6/(rf*cpf)
> 

a9 := B7*p1+B8*p2+B9*p3
> 

``
> 

a10 := 1+3*((p1*sigma4+p2*sigma5+p3*sigma6)/sigmaf-p1-p2-p3)/(2+(p1*sigma4+p2*sigma5+p3*sigma6)/((p1+p2+p3)*sigmaf)-((p1*sigma4+p2*sigma5+p3*sigma6)/sigmaf-p1-p2-p3))
> 

W := sum(b[i]*Y^i, i = 0 .. 3); Theta := sum(c[i]*Y^i, i = 0 .. 3); U := sum(d[i]*Y^i, i = 0 .. 2); Phi := sum(h[i]*Y^i, i = 0 .. 2)

Y^3*b[3]+Y^2*b[2]+Y*b[1]+b[0]

  

Y^3*c[3]+Y^2*c[2]+Y*c[1]+c[0]

  

Y^2*d[2]+Y*d[1]+d[0]

  

Y^2*h[2]+Y*h[1]+h[0]

 (2)
> 

F := a1*(1+1/bet)*(diff(W, `$`(Y, 2)))+a2*Ra*(diff(W, Y))+A-a5*M*W-S2*W^2+a2*Gr*Theta-S*betu*(W-U) = 0

9.1682928*Y*b[3]+3.0560976*b[2]+2.433571428*Y^2*b[3]+1.622380952*Y*b[2]+.8111904760*b[1]+1-1.346703274*b[3]*Y^3-1.346703274*b[2]*Y^2-1.346703274*b[1]*Y-1.346703274*b[0]-.5*(Y^3*b[3]+Y^2*b[2]+Y*b[1]+b[0])^2+.8111904760*c[3]*Y^3+.8111904760*c[2]*Y^2+.8111904760*c[1]*Y+.8111904760*c[0]+0.5e-1*d[2]*Y^2+0.5e-1*d[1]*Y+0.5e-1*d[0] = 0

 (3)
> 

T := (a4+Rd)*(diff(Theta, `$`(Y, 2)))+a3*Pr*Ra*(diff(Theta, Y))+Q*Theta+Pr*alp*S*bett*(Theta-Phi)+Pr*Ec*((1+1/bet)*a1*(diff(W, Y))^2+a5*M*W^2+(1+1/bet)*a1*S1*W^2+S2*W^3+S*betu*(W-U)) = 0

.205*c[1]*Y+.205*c[2]*Y^2+.205*c[3]*Y^3-.525*d[1]*Y-.525*d[2]*Y^2+.525*b[0]+.525*b[1]*Y+.525*b[2]*Y^2+.525*b[3]*Y^3+21.63764058*(Y^3*b[3]+Y^2*b[2]+Y*b[1]+b[0])^2-.105*h[0]+6.799682664*Y*c[3]+30.71903373*Y^2*c[3]+20.47935582*Y*c[2]-.105*Y^2*h[2]-.105*Y*h[1]-.525*d[0]+.205*c[0]+10.23967791*c[1]+2.266560888*c[2]+16.04451240*(3*Y^2*b[3]+2*Y*b[2]+b[1])^2+5.25*(Y^3*b[3]+Y^2*b[2]+Y*b[1]+b[0])^3 = 0

 (4)
> 

G := Ra*(diff(U, Y))+betu*(W-U) = 0

1.0*Y*d[2]+.5*d[1]+.5*b[3]*Y^3+.5*b[2]*Y^2-.5*d[2]*Y^2+.5*b[1]*Y-.5*d[1]*Y+.5*b[0]-.5*d[0] = 0

 (5)
> 

H := Ra*(diff(Phi, Y))+bett*(Theta-Phi) = 0

1.0*Y*h[2]+.5*h[1]+.5*c[3]*Y^3+.5*c[2]*Y^2-.5*Y^2*h[2]+.5*c[1]*Y-.5*Y*h[1]+.5*c[0]-.5*h[0] = 0

 (6)
> 

BCS := (D(W))(0) = 0, (D(Theta))(0) = 0, W(1) = -delta*(1+1/bet)*(D(W))(1), Theta(1) = 1+g*(D(Theta))(1), U(1) = -delta*(1+1/bet)*(D(W))(1), Phi(1) = 1+g*(D(Theta))(1)
> 

W := unapply(W(Y), Y)
> 

F := unapply(F(Y), Y)
> 

Theta := unapply(Theta(Y), Y)
> 

T := unapply(T(Y), Y)
> 

U := unapply(U(Y), Y)
> 

G := unapply(G(Y), Y)
> 

Phi := unapply(Phi(Y), Y)
> 

H := unapply(H(Y), Y)
> 

z1 := (D(W))(0) = 0

(D(W))(0) = 0

 (7)
> 

z2 := (D(Theta))(0) = 0

(D(Theta))(0) = 0

 (8)
> 

z3 := W(1) = -delta*(1+1/bet)*(D(W))(1)

b[3](1)+b[2](1)+b[1](1)+b[0](1) = -0.2e-2*(D(W))(1)

 (9)
> 

z4 := Theta(1) = 1+g*(D(Theta))(1)

c[3](1)+c[2](1)+c[1](1)+c[0](1) = 1+.1*(D(Theta))(1)

 (10)
> 

z5 := U(1) = -delta*(1+1/bet)*(D(W))(1)

d[2](1)+d[1](1)+d[0](1) = -0.2e-2*(D(W))(1)

 (11)
> 

z6 := Phi(1) = 1+g*(D(Theta))(1)

h[2](1)+h[1](1)+h[0](1) = 1+.1*(D(Theta))(1)

 (12)
> 

z7 := F(0)

1.+3.0560976*b[2](0)+.8111904760*b[1](0)-1.346703274*b[0](0)-.5*b[0](0)^2+.8111904760*c[0](0)+0.5e-1*d[0](0) = 0

 (13)
> 

z8 := T(0)

.525*b[0](0)+21.63764058*b[0](0)^2-.105*h[0](0)-.525*d[0](0)+.205*c[0](0)+10.23967791*c[1](0)+2.266560888*c[2](0)+16.04451240*b[1](0)^2+5.25*b[0](0)^3 = 0

 (14)
> 

z9 := G(0)

.5*d[1](0)+.5*b[0](0)-.5*d[0](0) = 0

 (15)
> 

z10 := H(0)

.5*h[1](0)+.5*c[0](0)-.5*h[0](0) = 0

 (16)
> 

z11 := F(1)

10.25516095*b[3](1)+3.331775278*b[2](1)-.5355127980*b[1](1)+1-1.346703274*b[0](1)-.5*(b[3](1)+b[2](1)+b[1](1)+b[0](1))^2+.8111904760*c[3](1)+.8111904760*c[2](1)+.8111904760*c[1](1)+.8111904760*c[0](1)+0.5e-1*d[2](1)+0.5e-1*d[1](1)+0.5e-1*d[0](1) = 0

 (17)
> 

z12 := T(1)

10.44467791*c[1](1)+22.95091671*c[2](1)+37.72371639*c[3](1)-.525*d[1](1)-.525*d[2](1)+.525*b[0](1)+.525*b[1](1)+.525*b[2](1)+.525*b[3](1)+21.63764058*(b[3](1)+b[2](1)+b[1](1)+b[0](1))^2-.105*h[0](1)-.105*h[2](1)-.105*h[1](1)-.525*d[0](1)+.205*c[0](1)+16.04451240*(3*b[3](1)+2*b[2](1)+b[1](1))^2+5.25*(b[3](1)+b[2](1)+b[1](1)+b[0](1))^3 = 0

 (18)
> 

z13 := G(1)

.5*d[2](1)+.5*b[3](1)+.5*b[2](1)+.5*b[1](1)+.5*b[0](1)-.5*d[0](1) = 0

 (19)
> 

z14 := H(1)

.5*h[2](1)+.5*c[3](1)+.5*c[2](1)+.5*c[1](1)+.5*c[0](1)-.5*h[0](1) = 0

 (20)
> 

NULL
> 

Z := fsolve([z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, z13, z14], {b[0], b[1], b[2], b[3], c[0], c[1], c[2], c[3], d[0], d[1], d[2], h[0], h[1], h[2]})

(21)
> 

"F(Y):=eval(sum(b[i]*Y^i,i=0..5),Z); "

Error, invalid input: eval received NULL, which is not valid for its 2nd argument, eqns

  
> 

"T(Y):=eval(sum(c[i]*Y^i,i=0..5),Z); "

Error, invalid input: eval received NULL, which is not valid for its 2nd argument, eqns

  
> 

"G(Y):=eval(sum(d[i]*Y^i,i=0..5),Z); "

Error, invalid input: eval received NULL, which is not valid for its 2nd argument, eqns

  
> 

"H(Y):=eval(sum(h[i]*Y^i,i=0..5),Z); "

Error, invalid input: eval received NULL, which is not valid for its 2nd argument, eqns

  
> 

NULL
> 

plot(F(Y), Y = 0 .. 1, axes = boxed, color = green, thickness = 2, labels = [Y, W])

Error, (in plot) unexpected options: [9.1682928*Y(Y)*b[3](Y)+3.0560976*b[2](Y)+2.433571428*Y(Y)^2*b[3](Y)+1.622380952*Y(Y)*b[2](Y)+.8111904760*b[1](Y)+1-1.346703274*b[3](Y)*Y(Y)^3-1.346703274*b[2](Y)*Y(Y)^2-1.346703274*b[1](Y)*Y(Y)-1.346703274*b[0](Y)-.5*(b[3](Y)*Y(Y)^3+b[2](Y)*Y(Y)^2+b[1](Y)*Y(Y)+b[0](Y))^2+.8111904760*c[3](Y)*Y(Y)^3+.8111904760*c[2](Y)*Y(Y)^2+.8111904760*c[1](Y)*Y(Y)+.8111904760*c[0](Y)+0.5e-1*d[2](Y)*Y(Y)^2+0.5e-1*d[1](Y)*Y(Y)+0.5e-1*d[0](Y) = 0, Y = 0 .. 1]

  
> 

plot(T(Y), Y = 0 .. 1, axes = boxed, color = green, thickness = 2, labels = [Y, Theta])

Error, (in plot) unexpected options: [.205*c[1](Y)*Y(Y)+.205*c[2](Y)*Y(Y)^2+.205*c[3](Y)*Y(Y)^3-.525*d[1](Y)*Y(Y)-.525*d[2](Y)*Y(Y)^2+.525*b[0](Y)+.525*b[1](Y)*Y(Y)+.525*b[2](Y)*Y(Y)^2+.525*b[3](Y)*Y(Y)^3+21.63764058*(b[3](Y)*Y(Y)^3+b[2](Y)*Y(Y)^2+b[1](Y)*Y(Y)+b[0](Y))^2-.105*h[0](Y)+6.799682664*Y(Y)*c[3](Y)+30.71903373*Y(Y)^2*c[3](Y)+20.47935582*Y(Y)*c[2](Y)-.105*Y(Y)^2*h[2](Y)-.105*Y(Y)*h[1](Y)-.525*d[0](Y)+.205*c[0](Y)+10.23967791*c[1](Y)+2.266560888*c[2](Y)+16.04451240*(3*Y(Y)^2*b[3](Y)+2*Y(Y)*b[2](Y)+b[1](Y))^2+5.25*(b[3](Y)*Y(Y)^3+b[2](Y)*Y(Y)^2+b[1](Y)*Y(Y)+b[0](Y))^3 = 0, Y = 0 .. 1]

  
> 

plot(G(Y), Y = 0 .. 1, axes = boxed, color = green, thickness = 2, labels = [Y, W])

Error, (in plot) unexpected options: [1.0*Y(Y)*d[2](Y)+.5*d[1](Y)+.5*b[3](Y)*Y(Y)^3+.5*b[2](Y)*Y(Y)^2-.5*d[2](Y)*Y(Y)^2+.5*b[1](Y)*Y(Y)-.5*d[1](Y)*Y(Y)+.5*b[0](Y)-.5*d[0](Y) = 0, Y = 0 .. 1]

  
> 

plot(H(Y), Y = 0 .. 1, axes = boxed, color = green, thickness = 2, labels = [Y, Theta])

Error, (in plot) unexpected options: [1.0*Y(Y)*h[2](Y)+.5*h[1](Y)+.5*c[3](Y)*Y(Y)^3+.5*c[2](Y)*Y(Y)^2-.5*Y(Y)^2*h[2](Y)+.5*c[1](Y)*Y(Y)-.5*Y(Y)*h[1](Y)+.5*c[0](Y)-.5*h[0](Y) = 0, Y = 0 .. 1]

  

NULL


 

Download AGM.mw
 

 

How to solve this PDE system ?...

Asked by: Prakash J 100
homework pde differential-equations
May 18 2023
0  3

eq1:=( d)/(dt)u+(d^(2))/(dy^(2))u + s*( d)/(dy)u + delta * theta = 0;

eq2:=( d)/(dt)theta + (d^(2))/(dy^(2))theta + s*Pr*( d)/(dy)theta +lambda* exp(theta/(1 +(epsilon*theta))) = 0; 

initial and boundary conditons   

t <=0; u = theta = 0, for 0 <= y  <= 1   

t> 0;  u =0, theta = 0   at  y = 0;  

t> 0;  u =1, theta = 0   at   y = 1  ;

where, s, epsilon, Pr, lambda, delta are arbitrary parameters

Error In Ode Solve ...

Asked by: KIRAN SAJJAN 40
ode syntax homework
May 13 2023
1  11

Hello 

How to remove this error 

3d_plots.mw

Impliment of Artificial Neural Network ...

Asked by: KIRAN SAJJAN 40
ode homework dsolve
April 27 2023
1  3

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.

How to implement finite element method for the giv...

Asked by: KIRAN SAJJAN 40
ode homework dsolve
April 24 2023
2  15
> 

  restart;
> 

  local gamma:
  local GAMMA:
> 

  odeSystem:= [ (1 + GAMMA)*diff(f(eta), eta$4) - S*(eta*diff(f(eta), eta$3) + 3*diff(f(eta), eta$2)
                +
                diff(f(eta), eta)*diff(f(eta), eta$2) - f(eta)*diff(f(eta), eta$3))
                -
                GAMMA*delta(2*diff(f(eta), eta$2)*diff(f(eta), eta$3)^2 + diff(f(eta), eta$2)^2*diff(f(eta), eta$4))
                -
                M^2*diff(f(eta), eta$2) = 0,

                (1 + (4*R)/3)*diff(theta(eta), eta$2) + Pr*S*(f(eta)*diff(theta(eta), eta)
                -
                eta*diff(theta(eta), eta) + Q*theta(eta)) = 0,

                diff(phi(eta), eta$2) + Sc*S*(f(eta)*diff(phi(eta), eta)
                -
                eta*diff(phi(eta), eta)) - Sc*gamma*phi(eta) = 0
              ];

  params:= [ S = 0.5, GAMMA = 0.1, delta = 0.1, gamma = 0.1, M = 1,
             Pr = 1, Ec = 0.2, Sc = 0.6, R = 1, Q = 1
           ];
  bcs :=[ f(0) = 0, (D@@2)(f)(0) = 0, f(1) = 1, D(f)(1) = 0, D(theta)(0) = 0,
          theta(1) = 1, phi(1) = 1, D(phi)(0) = 0
        ];

how to solve the equations by finite element method

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.

A simple question about sets...

Asked by: Kitonum 21540
inequality equality uniqueness
March 24 2023
1  4

When we specify a set (a sequence of objects enclosed in curly braces), Maple removes duplicates, since the elements of the set must be unique, that is, they cannot be repeated. See below for 2 examples. With the first example  {a<=b  and  b>=a}, everything is in order, since they are one and the same. But Maple treats the same equality, written in two ways  {a=b, b=a} , as different objects. It seems to me that this is not very convenient:

restart;
{a<=b, b>=a}; # OK
{a=b, b=a}; # not OK
is((a=b)=(b=a)); # not OK

                                                  

 

how to solve numerical solution of ODE with Bc and...

Asked by: KIRAN SAJJAN 40
ode homework dsolve
February 22 2023
0  16

restart;
kp := .3;

Pr := .3; N := .5; g := .5; A := 1; B := 0; M := .5; lambda := .5; Ec := .5;

rf := 997.1; kf := .613; cpf := 4179; `&sigma;f` := 0.5e-1;
p1 := 0.1e-1; sigma1 := 2380000; rs1 := 4250; ks1 := 8.9538; cps1 := 686.2;
p2 := 0.5e-1; sigma2 := 3500000; rs2 := 10500; ks2 := 429; cps2 := 235;

NULL;
a1 := (1-p1)^2.5*(1-p2)^2.5;
a2 := (1-p2)*(1-p1+p1*rs1/rf)+p2*rs2/rf;
a3 := 1+3*((p1*sigma1+p2*sigma2)/`&sigma;f`-p1-p2)/(2+(p1*sigma1+p2*sigma2)/((p1+p2)*`&sigma;f`)-((p1*sigma1+p2*sigma2)/`&sigma;f`-p1-p2));

a4 := (1-p2)*(1-p1+p1*rs1*cps1/(rf*cpf))+p2*rs2*cps2/(rf*cpf);
a5 := (ks1+2*kf-2*p1*(kf-ks1))*(ks2+2*kf*(ks1+2*kf-2*p1*(kf-ks1))/(ks1+2*kf+p1*(kf-ks1))-2*p2*(kf*(ks1+2*kf-2*p1*(kf-ks1))/(ks1+2*kf+p1*(kf-ks1))-ks2))/((ks1+2*kf+p1*(kf-ks1))*(ks2+2*kf*(ks1+2*kf-2*p1*(kf-ks1))/(ks1+2*kf+p1*(kf-ks1))+2*p2*(kf*(ks1+2*kf-2*p1*(kf-ks1))/(ks1+2*kf+p1*(kf-ks1))-ks2)));


OdeSys := (diff(U(Y), Y, Y))/(a1*a2)+Theta(Y)+N*(Theta(Y)*Theta(Y))-a3*(M*M)*U(Y)/a2-(kp*kp)*U(Y)/(a1*a2), a5*(diff(Theta(Y), Y, Y))/a4+Pr*Ec*((diff(U(Y), Y))^2+U(Y)^2*(kp*kp))/(a1*a2); Cond := U(0) = lambda*(D(U))(0), Theta(0) = A+g*(D(Theta))(0), U(1) = 0, Theta(1) = B; Ans := dsolve([OdeSys, Cond], numeric, output = listprocedure);
U := proc (Y) options operator, arrow, function_assign; (eval(U(Y), Ans))(0) end proc;
                 U := Y -> (eval(U(Y), Ans))(0)
Theta := proc (Y) options operator, arrow, function_assign; (eval(Theta(Y), Ans))(0) end proc;
             Theta := Y -> (eval(Theta(Y), Ans))(0)
Theta_b := (int(U(Y)*Theta(Y), Y = 0 .. 1))/(int(U(Y), Y = 0 .. 1));
Error, (in Theta) too many levels of recursion
Q := int(U(Y), Y = 0 .. 1, numeric);
Error, (in Theta) too many levels of recursion
NUMERIC := [(eval((diff(U(Y), Y))/a1, Ans))(0), (eval(-(diff(Theta(Y), Y))/(Theta_b*a5), Ans))(0)];
Error, (in Theta) too many levels of recursion

 

i need the solution  for Y=0 and Y=1

How to plot stream lines and isotherms for the giv...

Asked by: KIRAN SAJJAN 40
ode homework differential-equations
February 21 2023
1  9

Streamlines, isotherms and microrotations for Re = 1, Pr = 7.2, Gr = 105 and (a) Ha = 0 (b) Ha = 30 (c) Ha = 60 (d) Ha = 100.

 

Fig. 2

for Ra = 105, Ha = 50, Pr = 0.025 and θ = 1 − Y

 

 

eqat := {M . (D(theta))(0)+2.*Pr . f(0) = 0, diff(phi(eta), eta, eta)+2.*Sc . f(eta) . (diff(phi(eta), eta))-(1/2)*S . Sc . eta . (diff(phi(eta), eta))+N[t]/N[b] . (diff(theta(eta), eta, eta)) = 0, diff(g(eta), eta, eta)-2.*(diff(f(eta), eta)) . g(eta)+2.*f(eta) . (diff(g(eta), eta))-S . (g(eta)+(1/2)*eta . (diff(g(eta), eta)))-1/(sigma . Re[r]) . ((1+d^%H . exp(-eta))/(1+d . exp(-eta))) . g(eta)-beta^%H . ((1+d^%H . exp(-eta))^2/sqrt(1+d . exp(-eta))) . g(eta) . sqrt((diff(f(eta), eta))^2+g(eta)^2) = 0, diff(theta(eta), eta, eta)+2.*Pr . f(eta) . (diff(theta(eta), eta))-(1/2)*S . Pr . eta . (diff(theta(eta), eta))+N[b] . Pr . ((diff(theta(eta), eta)) . (diff(phi(eta), eta)))+N[t] . Pr . ((diff(theta(eta), eta))^2)+4/3 . N . (diff((C[T]+theta(eta))^3 . (diff(theta(eta), eta)), eta)) = 0, diff(f(eta), eta, eta, eta)-(diff(f(eta), eta))^2+2.*f(eta) . (diff(f(eta), eta))+g(eta)^2-S . (diff(f(eta), eta)+(1/2)*eta . (diff(f(eta), eta, eta)))-1/(sigma . Re[r]) . ((1+d^%H . exp(-eta))/(1+d . exp(-eta))) . (diff(f(eta), eta))-beta^%H . ((1+d^%H . exp(-eta))^2/sqrt(1+d . exp(-eta))) . (diff(f(eta), eta)) . sqrt((diff(f(eta), eta))^2+g(eta)^2) = 0, g(0) = 1, g(6) = 0, phi(0) = 1, phi(6) = 0, theta(0) = 1, theta(6) = 0, (D(f))(0) = 1, (D(f))(6) = 0};
sys1 := eval(eqat, {M = 0, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, beta^%H = .2, d^%H = 1.5});
sys2 := eval(eqat, {M = 0, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, beta^%H = .4, d^%H = 1.5});
sys3 := eval(eqat, {M = 0, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, beta^%H = .6, d^%H = 1.5});
sys4 := eval(eqat, {M = 0, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, beta^%H = .8, d^%H = 1.5});
sys5 := eval(eqat, {M = .5, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, beta^%H = .2, d^%H = 1.5});
sys6 := eval(eqat, {M = .5, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, beta^%H = .4, d^%H = 1.5});
sys7 := eval(eqat, {M = .5, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, beta^%H = .6, d^%H = 1.5});
sys8 := eval(eqat, {M = .5, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, beta^%H = .8, d^%H = 1.5});
sys9 := eval(eqat, {M = 1, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, beta^%H = .2, d^%H = 1.5});
sys10 := eval(eqat, {M = 1, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, beta^%H = .4, d^%H = 1.5});
sys11 := eval(eqat, {M = 1, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, beta^%H = .6, d^%H = 1.5});
sys12 := eval(eqat, {M = 1, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, beta^%H = .8, d^%H = 1.5});
sys13 := eval(eqat, {M = 1.5, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, beta^%H = .2, d^%H = 1.5});
sys14 := eval(eqat, {M = 1.5, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, beta^%H = .4, d^%H = 1.5});
sys15 := eval(eqat, {M = 1.5, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, beta^%H = .6, d^%H = 1.5});
sys16 := eval(eqat, {M = 1.5, N = 2, Pr = .8, S = -2.5, Sc = .5, d = 2, sigma = .2, C[T] = .5, N[b] = .4, N[t] = .4, Re[r] = 1.1, beta^%H = .8, d^%H = 1.5});
 

Can we solve nonlinear coupled Ode with Bc?...

Asked by: KIRAN SAJJAN 40
ode homework dsolve
February 16 2023
1  4

restart;

OdeSys := diff(U(Y), Y, Y)+Theta(Y)+N*(Theta(Y)*Theta(Y))-(M*M)*U(Y) = 0, diff(Theta(Y), Y, Y)+E*(diff(U(Y), Y))^2 = 0;

Cond := U(0) = lambda*(D(U))(0), Theta(0) = A+g*(D(Theta))(0), U(1) = 0, Theta(1) = B; sys := [OdeSys, Cond];
Ans := dsolve(sys);

I Encountered Error Message trying to use dsolve t...

Asked by: Elisha 50
ode parameters dsolve
February 11 2023
0  6

I find it difficult to use dsolve to solve system of ordinary differential equations with assigned parameters and initial conditions. The error message "Error, (in dsolve/numeric) 'parameters' must be specified as a list of unique unassigned names" kept coming up.

Pls see the uploaded equation for more understanding

> 

restart
> 

interface(imaginaryunit = F)

I

 (1)
> 

I

I

 (2)
> 

sqrt(-4)

2*I

 (3)
> 

NULL
> 

Suscep := diff(S(t), t) = theta*epsilon+v__2*S__v(t)-S(t)*lambda-S(t)*(µ+v__1)

diff(S(t), t) = theta*varepsilon+v__2*S__v(t)-S(t)*lambda-S(t)*(µ+v__1)

 (4)
> 

Vacc := diff(S__v(t), t) = (1-theta)*epsilon+v__1*S(t)-(µ+alpha+v__2)*S__v(t)-(1-w)*S__v(t)*lambda
> 

Immun := diff(V(t), t) = alpha*S__v(t)+`&rho;__A`*A(t)+(1-k)*`&rho;__Q`*Q(t)+`&rho;__I`*(I)(t)-µ*V(t)
> 

Exp := diff(E(t), t) = S(t)*lambda+(1-w)*S__v(t)*lambda-(q__E+delta+µ)*E(t)
> 

Asymp := diff(A(t), t) = delta*a*E(t)-(`&rho;__A`+µ)*A(t)+k*`&rho;__Q`*Q(t)
> 

Inf := diff((I)(t), t) = delta*(1-a)*E(t)-(`&rho;__I`+q__I+`&delta;__I`+µ)*(I)(t)
> 

Quar := diff((I)(t), t) = q__E*E(t)+q__I*(I)(t)-(`&rho;__Q`+`&delta;__Q`+µ)*Q(t)
> 

init_conds := S(0) = S_0, S__v(0) = S__v*_0, V(0) = V_0, E(0) = E_0, A(0) = A_0, (I)(0) = I_0, Q(0) = Q_0

S(0) = S_0, S__v(0) = S__v*_0, V(0) = V_0, E(0) = E_0, A(0) = A_0, I(0) = I_0, Q(0) = Q_0

 (5)
> 

sys := {Asymp, Exp, Immun, Inf, Quar, Suscep, Vacc, init_conds}
> 

``
> 

sol := dsolve(sys, numeric, parameters = [`&delta;__Q`, `&delta;__I`, a, k, epsilon, v[1], q[E], q[I], q[A], eta[A], eta[Q], rho[A], rho[Q], rho[I], v[2], alpha, mu, delta, alpha, beta, w, lambda, S_0, S__v*_0, V_0, E_0, A_0, I_0, Q_0], method = rkf45)

Error, (in dsolve/numeric) 'parameters' must be specified as a list of unique unassigned names

  
> 

sol(parameters = [delta = .125, `&delta;__Q` = 0.6847e-3, epsilon = .464360344, `&delta;__I` = 0.2230e-8, a = .6255, q[E] = 0.18113e-3, k = .15, v__1 = 0.5e-1, v__2 = 0.6e-1, `&rho;__Q` = 0.815e-1, `&rho;__A` = .1, `&rho;__I` = 0.666666e-1, q__I = 0.1923e-2, q__A = 0.4013e-7, `&eta;__A` = .1213, `&eta;__Q` = 0.3808e-2*alpha and 0.3808e-2*alpha = .4, w = .5925, mu = 0.464360344e-4, lambda = 0.1598643e-7, S_0 = 1.0, S__v*_0 = 0.6e-4, V_0 = 0.35e-4, E_0 = 0.5e-4, I_0 = 0.32e-4, A_0 = 0.15e-4, Q_0 = 0.1e-4])

sol(parameters = [delta = .125, delta__Q = 0.6847e-3, varepsilon = .464360344, delta__I = 0.2230e-8, a = .6255, q[E] = 0.18113e-3, k = .15, v__1 = 0.5e-1, v__2 = 0.6e-1, rho__Q = 0.815e-1, rho__A = .1, rho__I = 0.666666e-1, q__I = 0.1923e-2, q__A = 0.4013e-7, eta__A = .1213, false, w = .5925, mu = 0.464360344e-4, lambda = 0.1598643e-7, S_0 = 1.0, S__v*_0 = 0.6e-4, V_0 = 0.35e-4, E_0 = 0.5e-4, I_0 = 0.32e-4, A_0 = 0.15e-4, Q_0 = 0.1e-4])

 (6)
> 

Evaluate*the*system*at*t = 2
> 

sol(2)

sol(2)

 (7)
> 

sol(1)

sol(1)

 (8)
> 

sol(.1)

sol(.1)

 (9)
> 

sol(.3)

sol(.3)

 (10)
> 

sol(.5)

sol(.5)

 (11)
> 

sol(.7)

sol(.7)

 (12)
> 

sol(.9)

sol(.9)

 (13)
> 

sol(1.1)

sol(1.1)

 (14)
> 

sol(1.3)

sol(1.3)

 (15)
> 

sol(1.5)

sol(1.5)

 (16)
> 

 
> 

 

Download Covid19_Simulation.mw

To find the table values of Nusselt and Skin frict...

Asked by: KIRAN SAJJAN 40
February 10 2023
0  1

odeSys := {diff(Theta(x), x, x)+Pr*(R*(diff(Theta(x), x))*f(x)+Nb*(diff(Theta(x), x))*(diff(Phi(x), x))+Nt*(diff(Theta(x), x))^2), N2*(diff(G(x), x, x))-N1*(2*G(x)+diff(f(x), x, x))-N3*R*((diff(f(x), x))*G(x)-f(x)*(diff(G(x), x))), diff(Phi(x), x, x)+R*Sc*f(x)*(diff(Phi(x), x))+Nt*(diff(Theta(x), x, x))/Nb, (1+N1)*(diff(g(x), x, x))+R*((diff(g(x), x))*f(x)-g(x)*(diff(f(x), x)))-M*g(x)+2*Kr*(diff(f(x), x)), (1+N1)*(diff(f(x), x, x, x, x))-R*((diff(f(x), x))*(diff(f(x), x, x))-f(x)*(diff(f(x), x, x, x)))+N1*(diff(G(x), x, x))-M*(diff(f(x), x, x))-2*Kr*(diff(g(x), x))}; cond := f(0) = 0, (D(f))(0) = 1, g(0) = 0, Theta(0) = 1, G(0) = -n*((D@@2)(f))(0), Phi(0) = 1, f(1) = lambda, (D(f))(1) = 0, g(1) = 0, Theta(1) = 0, G(1) = n*((D@@2)(f))(1), Phi(1) = 0; ans := {};

n := .5; N1 := 0.; N2 := 1.0; N3 := .1; lambda := .1; M := .1; Kr := .1; Sc := 1.0; Nb := .1; Pr := 1.0; Nt := .1; R := .5;

ans := dsolve*{cond, eval*odeSys};

hello these are the pde and Boundary conditions  i want to calculate the value of f''(0) ,Theta(0) and  Phi(0)

what is the proper cammand to get the table values for the given equation
NBVs := [eval(ans(N1*G(x)+(1+N1)*(diff(f(x), x, x))), x = 0), eval(ans(-(diff(Theta(x), x))), x = 0), eval(ans(-(diff(Phi(x), x))), x = 0)];

FEM or FDM for the given pde can i calculate the ...

Asked by: KIRAN SAJJAN 40
February 07 2023
0  1

Hi,

I want to solve system of PDE equations by maple and i dont know how can i write it codes that can solve them for me. Can you create the code for the equation

Thank you

A Maple Programme Code...

Asked by: abiodunowoyemi9 30
February 06 2023
0  2

Good day,
 

1. Please I need your greatest help. Can anyone please help me to run the examples on the attached papers on Maple software?

 2. Also help me to plot the graphs along with the exact solution

 3. If possible with tables

 I tried but did not get the results as expected. I shall be very grateful if I can get assistance from you

 

Thanks
 

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