Maple 18 Questions and Posts

These are Posts and Questions associated with the product, Maple 18

restart

with(PolynomialIdeals):

``

``

randomzero := proc (ListVar) local A, G, i, lm, B, f, g; option trace; A := ListVar; G := NULL; for i to nops(A) do f := A[i]^(i+1)+randpoly([op(`minus`({op(A)}, {A[i]}))], terms = 1, coeffs = rand(-4 .. -1), degree = i); G := G, f end do; print(IsZeroDimensional(`<,>`(G))); RETURN([G]) end proc:

randomzero([x, y])

{--> enter randomzero, args = [x, y]

 

[x, y]

 

"G:="

 

x^2-y-4

 

x^2-y-4

 

y^3-3*x

 

x^2-y-4, y^3-3*x

 

true

 

<-- exit randomzero (now at top level) = [x^2-y-4, y^3-3*x]}

 

[x^2-y-4, y^3-3*x]

(1)

``

Download bug.mw

Hi

I think there is a bug in the "randpoly" command. please see the attached file line 7 of my procedure "randomzero". Why x^2-y-4 is created while terms=1 is considered and the outputs must contain binomial?

How to get U1,U2,..I dont know how to use this inverse transform.Please help to find the series.

CM.mw

Equilibrium._solutions.mw

I need to obtain the equilibrium solutions when infection is present as well as analyze the local asymptotic stability when infection is absent and present in the system

Hi, please can someone help on how non-dimensionalize PDEs. 

I have tried the following, but is not working:

restart:
eqn := (diff(theta(x, z, t), x))^2*(K[1]-K[3])*cos(theta(x, z, t))*sin(theta(x, z, t))+(diff(theta(x, z, t), x))*((diff(theta(x, z, t), z))*(-K[1]*cos(2*theta(x, z, t))+K[3]*cos(2*theta(x, z, t)))-(1/2)*gamma[1]*(4*sin(theta(x, z, t))^2*u(x, z, t)+2*u(x, z, t)*cos(2*theta(x, z, t))))+(diff(theta(x, z, t), z))^2*(K[3]-K[1])*cos(theta(x, z, t))*sin(theta(x, z, t))-(1/2)*gamma[1]*(diff(theta(x, z, t), z))*(4*sin(theta(x, z, t))^2*v(x, z, t)+2*v(x, z, t)*cos(2*theta(x, z, t)))+(diff(theta(x, z, t), z, x))*(-2*K[1]+2*K[3])*cos(theta(x, z, t))*sin(theta(x, z, t))-(diff(u(x, z, t), z))*((1/2)*gamma[2]*cos(2*theta(x, z, t))+(1/2)*gamma[1]*(2*sin(theta(x, z, t))^2+cos(2*theta(x, z, t))))-(diff(v(x, z, t), x))*((1/2)*gamma[2]*cos(2*theta(x, z, t))+(1/2)*gamma[1]*(-2*sin(theta(x, z, t))^2-cos(2*theta(x, z, t))))-(1/2)*gamma[1]*(4*sin(theta(x, z, t))^2*(diff(theta(x, z, t), t))+2*(diff(theta(x, z, t), t))*cos(2*theta(x, z, t)))+((diff(u(x, z, t), x))*gamma[2]-(diff(v(x, z, t), z))*gamma[2])*cos(theta(x, z, t))*sin(theta(x, z, t))+f[2](theta(x, z, t))*(diff(theta(x, z, t), x, x))+f[1](theta(x, z, t))*(diff(theta(x, z, t), z, z));

varchange := {t = T*tau, u = xi*h^2*U/alpha[4], v = xi*h^2*V/alpha[4], x = X*h, z = Z*h, K[3] = K[1]*k[3], f[1] = K[1]*F[1], f[2] = K[1]*F[2], gamma[1] = mu*Gamma[1], gamma[2] = mu*Gamma[2]};

PDEtools:-dchange(varchange, eqn, [tau, U, V, X, Z, k[3], F[1], F[2], GAMMA[1], GAMMA[2]]);

i want to label x,y axis with command...if i use manually ..i always need to do again after running..so how can i label x,y axis in this plot...? i watch manual and i din't find for axis..stress-strain.mwstress-strain.mw

in this equations...how to plot (a,e)? thank you guys

plot.mw

Can you change f(eta) to upflow curve and theta(eta) to downflow curve.

In my Problem,Boundary Conditions are

theta(infinity) = 0, (D(f))(infinity) = 1 , (Take, eta =infinity)

Flows will be correct for what value is taken for infinity .

I take  eta = 5. and also tried changing ranges  but could't find it.Please Help to fix the curve.

my code is,

SM.mw

How to solve ordinary differemtial equation system with initial conditions and boundary conditions. Here, some initial conditions are unknown variables. So how to find these  values of parameters.

eq1 := diff(f(x), x, x, x)+(1/2)*cos(alpha)*x*(diff(f(x), x, x))+(1/2)*sin(alpha)*f(x)*(diff(f(x), x, x)) = 0;

eq2 := diff(g(x), x, x)+diff(g(x), x)+(diff(g(x), x))*(diff(h(x), x))+cos(alpha)*x*(diff(g(x), x))+sin(alpha)*f(x)*g(x) = 0;

eq3 := diff(g(x), x, x)+diff(h(x), x, x)+1/2*(cos(alpha)*x+sin(alpha)*f(x)) = 0

ics:=f(0)=0, f'(0)=1, f''(0)=a[1], g(0)=1, g'(0)=a[2], h(0)=1, h'(0)=a[3];

bcs:=f(x) , g(x), h(x) tends to 0 ad x tends to infinity

How to find series values.I got this error.Please Help.

Maple code for the problem is

TFBE.mw

  Could you please give maple code for Shooting Method/Kellor box Method or any numerical method except RK Method to this system of Differential Equations.

SMMS.mw

Please help me to solve this error.   or

Can you give the maple code for Shooting method/ Kellor Box Method for this problem.

mvp-1.mw

How do I label the curves in Maple graph.

Please, I need commands to tweak my maple 18 graph.

I have some ODE system contains unknown variables with  boundary conditions  (see the attachment). How to solve these system and find the vales of unknown variables.

In this problem, the boundary conditions tends to 0, when x tends to infinity.  BVP_with_parameters.mw
 

restart

eq1 := f(x) = x+a[1]*x^2-(1/48)*sqrt(2)*a[1]*x^4-(1/120)*a[1]^2*sqrt(2)*x^5;

h(x) = -0.3535533905e-3*x^5*a[2]*a[1]*a[3]-0.3333333334e-9*x^5*a[3]*a[2]^4+0.4166666668e-7*x^4*a[2]*a[3]^3-0.3333333334e-9*x^5*a[2]^2*a[3]^3-0.5000000000e-9*x^5*a[3]^2*a[2]^3+0.1250000000e-6*x^4*a[3]*a[2]^3-0.8333333336e-10*x^5*a[2]*a[3]^4+0.1250000000e-6*x^4*a[3]^2*a[2]^2-0.8333333336e-10*x^5*a[2]^5+0.4166666668e-7*x^4*a[2]^4+a[3]*x-0.1473139128e-1*x^4*a[1]*a[3]+0.2946278254e-1*x^4*a[1]*a[2]-0.3240906080e-3*x^5*a[1]*a[2]^2+0.2798964342e-5*x^5*a[2]*a[3]^2+0.4714045206e-5*x^5*a[3]*a[2]^2-0.6629126071e-3*x^4*a[3]*a[2]+0.7812499998e-3*x^5*a[3]-0.2946278254e-1*x^3*a[3]-0.5892556508e-3*x^4*a[2]^2+0.1915080866e-5*x^5*a[2]^3+0.5892556509e-1*x^3*a[2]-0.4687500000e-2*x^5*a[2]+0.5000000000e-2*a[2]^2*x^2-0.1666666667e-4*x^3*a[2]^3+0.5000000000e-2*a[2]*x^2*a[3]-0.3333333334e-4*x^3*a[3]*a[2]^2-0.1666666667e-4*x^3*a[2]*a[3]^2+1.

(1)

bcs := f(0) = 0, (D(f))(0) = 1, f(10) = 0, g(0) = 1, g(10) = 0, h(0) = 1, h(10) = 0;

f(0) = 0, (D(f))(0) = 1, f(10) = 0, g(0) = 1, g(10) = 0, h(0) = 1, h(10) = 0

(2)

sol := dsolve([{f(x), g(x), h(x)}, bcs], numeric)

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

 

``

 

Greetings! I have solved a nonlinear equation by Newton iterative method. Now i want to plot basins of attraction. Being a beginner, I have no clue how to plot it? Its totally different rom other simple plotting commands. Need help in this regard.Thank

I'm new in maple.I'm just learning, i couldn't get the solution.Please help me to solve this Error.

Here is my code.

sps-RK_Method.mw

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