Maple 18 Questions and Posts

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

Dear maple users 

Greetings.

I hope you are all fine.

In this code, I am solving the PDEs via pdsolve with numeric.

There is some mistake in the boundary condition and pdsolve.

Kindly help me that to get the solution for this PDE.

Waiting for your reply.

In this problem h(z) is piecewise 

 

Bc:   

code:JVB.mw

 

Note: z=0.5:

Hi everyone, i want to draw 3d graphics of fractional solution with given by Mittag Leffler function in cantor sets. I want to see like this graphic. I added maple file. Thanks in advance.

3D_graphic.mw3D_graphic.mw

Hi, dear community,
I have a Maple package "rath" for finding the traveling wave solution of differential equations. But I am not able to loading in Maple 18. Please see this attached zip folder and need help in this regard.
Kind regard

inform.txt,

PaperExp.mws

rath.txt

How to plot u(t)= z'(t) with respect to x, y, z?

  Here,  z(t)=y'(t), y(t)=x'(t).

where, x(t)= z^3(t), y(t)= z^3(t)/2, z(t) = (a- b), a, b are time interval.

Trajectories.mw

How to solve the matrix for u(t) and plot phase trajector?

Hello!

I have a difficulty with a function used in procedure. The procedure uses a multivariable function and if the specific choice of the function is not made the procedure seems to give proper result, but In case I make a specific choice of the function and then try use this procedure gives me incorrect result.

To be more exact I use Physics package (there is a need to calcute combinations of covariant derivates ). The calculations are performed in a curved space with a defined metric.

So here is the procedure:

SD2 := proc (psi) SumOverRepeatedIndices(g_[`~kappa`, `~lambda`]*(d_[kappa](d_[lambda](psi(X)))-Christoffel[`~sigma`, kappa, lambda]*d_[sigma](psi(X))))^2-SumOverRepeatedIndices(g_[`~kappa`, `~rho`]*(d_[kappa](d_[lambda](psi(X)))-Christoffel[`~sigma`, kappa, lambda]*d_[sigma](psi(X)))*g_[`~lambda`, `~tau`]*(d_[rho](d_[tau](psi(X)))-Christoffel[`~gamma`, rho, tau]*d_[gamma](psi(X)))) end proc;

If I turn to the procedure :

SD2(psi);

the result is  correct.

But  then I specify a psi function:

psi:=(t,r,x,y,z)->chi(r)+q*t;(here q is supposed to be a constant)

and turn to the procedure once again:

SD2(psi);

It gives me a wrong result.

I don't know what is the reason.

Thank you.

 

 

Download MHD1.mw

 

 

System of equations with boundary conditions are moving?

Also, find the values of unknown variables?

Hey everyone,

f_1 and f_2  are satisfying the set of non-linear integral equations I have attached to this message.
I know that I need to solve them numerically by iterations. Probably, the first guest of the function f_1 and f_2  is the driving term. a is just a parameter which can be fixed (I guess smaller than \pi/4). * is the convolution product and k is the momentum space parameter. I learnt that in order to solve them I should solve them in the Fourier space. I know also that I need to discretize these function in the “real ” space between {-L,+L} before applying the FFT or one of its relatives. Thank you for any suggestions or leads.


 

restart;

M__h := 0.352e-1;

0.352e-1

 

0.34e-1

 

0.8354e-1

 

0.96e-2

 

.123

 

0.7258e-1

 

0.214e-1

 

0.219e-1

 

.123

 

.7902

 

.11

 

0.136e-3

 

0.5e-1

 

0.8910e-1

 

0.45e-1

 

.7

 

.7214

 

1.354

 

0.235e-1

(1)

pdes := [diff(B(t, x), t) = M__h-beta__1*B(t, x)*G(t, x)/N__h+beta__2*B(t, x)*G(t, x)/N__h-mu__h*B(t, x)+sigma__h*E(t, x)*(diff(B(t, x), x, x)), diff(C(t, x), t) = beta__1*B(t, x)*G(t, x)/N__h-u[1]*C(t, x)/(1+C(t, x))-mu__h*C(t, x)*(diff(C(t, x), x, x)), diff(DD(t, x), t) = beta__2*DD(t, x)*G(t, x)/N__h-u[1]*DD(t, x)/(1+DD(t, x))-mu__h*DD(t, x)-delta__1*DD(t, x)*(diff(DD(t, x), x, x)), diff(E(t, x), t) = u[1]*C(t, x)/(1+C(t, x))+u[1]*DD(t, x)/(1+DD(t, x))-(mu__h+sigma__h)*E(t, x)*(diff(E(t, x), x, x)), diff(F(t, x), t) = M__b-beta__3*F(t, x)*C(t, x)/N__b+beta__4*F(t, x)*DD(t, x)/N__b-mu__b*F(t, x)*(diff(F(t, x), x, x)), diff(G(t, x), t) = beta__3*F(t, x)*C(t, x)/N__b+beta__4*F(t, x)*DD(t, x)/N__b-mu__b*G(t, x)*(diff(G(t, x), x, x))];

[diff(B(t, x), t) = 0.352e-1-0.891056911e-1*B(t, x)*G(t, x)-0.96e-2*B(t, x)+0.8910e-1*E(t, x)*(diff(diff(B(t, x), x), x)), diff(C(t, x), t) = .6791869919*B(t, x)*G(t, x)-0.45e-1*C(t, x)/(1+C(t, x))-0.96e-2*C(t, x)*(diff(diff(C(t, x), x), x)), diff(DD(t, x), t) = .5900813008*DD(t, x)*G(t, x)-0.45e-1*DD(t, x)/(1+DD(t, x))-0.96e-2*DD(t, x)-0.235e-1*DD(t, x)*(diff(diff(DD(t, x), x), x)), diff(E(t, x), t) = 0.45e-1*C(t, x)/(1+C(t, x))+0.45e-1*DD(t, x)/(1+DD(t, x))-0.9870e-1*E(t, x)*(diff(diff(E(t, x), x), x)), diff(F(t, x), t) = .7214-.1739837398*F(t, x)*C(t, x)+.1780487805*F(t, x)*DD(t, x)-1.354*F(t, x)*(diff(diff(F(t, x), x), x)), diff(G(t, x), t) = .1739837398*F(t, x)*C(t, x)+.1780487805*F(t, x)*DD(t, x)-1.354*G(t, x)*(diff(diff(G(t, x), x), x))]

(2)

bcs := [(D[2](B))(t, 0) = 0, (D[2](B))(t, 1) = 0, (D[2](C))(t, 0) = 0, (D[2](C))(t, 1) = 0, (D[2](DD))(t, 0) = 0, (D[2](DD))(t, 1) = 0, (D[2](E))(t, 0) = 0, (D[2](E))(t, 1) = 0, (D[2](F))(t, 0) = 0, (D[2](F))(t, 1) = 0, (D[2](G))(t, 0) = 0, (D[2](G))(t, 1) = 0, B(0, x) = 100, C(0, x) = 70, DD(0, x) = 50, E(0, x) = 70, F(0, x) = 100, G(0, x) = 70]

[(D[2](B))(t, 0) = 0, (D[2](B))(t, 1) = 0, (D[2](C))(t, 0) = 0, (D[2](C))(t, 1) = 0, (D[2](DD))(t, 0) = 0, (D[2](DD))(t, 1) = 0, (D[2](E))(t, 0) = 0, (D[2](E))(t, 1) = 0, (D[2](F))(t, 0) = 0, (D[2](F))(t, 1) = 0, (D[2](G))(t, 0) = 0, (D[2](G))(t, 1) = 0, B(0, x) = .100, C(0, x) = .70, DD(0, x) = .50, E(0, x) = .70, F(0, x) = .100, G(0, x) = .70]

(3)

sol := pdsolve(pdes, bcs, numeric);

module () local INFO; export plot, plot3d, animate, value, settings; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; end module

(4)

sol:-plot3d([B(t, x), C(t, x)], t = 0 .. 20, x = 0 .. 20)

Error, (in pdsolve/numeric/plot3d) unable to compute solution for t>HFloat(0.25):
Newton iteration is not converging

 

``


 

Download spatial_1.mw


 

restart;

M__h := 0.352e-1;

0.352e-1

 

0.34e-1

 

0.8354e-1

 

0.96e-2

 

.123

 

0.7258e-1

 

0.214e-1

 

0.219e-1

 

.123

 

.7902

 

.11

 

0.136e-3

 

0.5e-1

 

0.8910e-1

 

0.45e-1

 

.7

 

.7214

 

1.354

 

0.235e-1

(1)

pdes := [diff(B(t, x), t) = M__h-beta__1*B(t, x)*G(t, x)/N__h+beta__2*B(t, x)*G(t, x)/N__h-mu__h*B(t, x)+sigma__h*E(t, x)*(diff(B(t, x), x, x)), diff(C(t, x), t) = beta__1*B(t, x)*G(t, x)/N__h-u[1]*C(t, x)/(1+C(t, x))-mu__h*C(t, x)*(diff(C(t, x), x, x)), diff(DD(t, x), t) = beta__2*DD(t, x)*G(t, x)/N__h-u[1]*DD(t, x)/(1+DD(t, x))-mu__h*DD(t, x)-delta__1*DD(t, x)*(diff(DD(t, x), x, x)), diff(E(t, x), t) = u[1]*C(t, x)/(1+C(t, x))+u[1]*DD(t, x)/(1+DD(t, x))-(mu__h+sigma__h)*E(t, x)*(diff(E(t, x), x, x)), diff(F(t, x), t) = M__b-beta__3*F(t, x)*C(t, x)/N__b+beta__4*F(t, x)*DD(t, x)/N__b-mu__b*F(t, x)*(diff(F(t, x), x, x)), diff(G(t, x), t) = beta__3*F(t, x)*C(t, x)/N__b+beta__4*F(t, x)*DD(t, x)/N__b-mu__b*G(t, x)*(diff(G(t, x), x, x))];

[diff(B(t, x), t) = 0.352e-1-0.891056911e-1*B(t, x)*G(t, x)-0.96e-2*B(t, x)+0.8910e-1*E(t, x)*(diff(diff(B(t, x), x), x)), diff(C(t, x), t) = .6791869919*B(t, x)*G(t, x)-0.45e-1*C(t, x)/(1+C(t, x))-0.96e-2*C(t, x)*(diff(diff(C(t, x), x), x)), diff(DD(t, x), t) = .5900813008*DD(t, x)*G(t, x)-0.45e-1*DD(t, x)/(1+DD(t, x))-0.96e-2*DD(t, x)-0.235e-1*DD(t, x)*(diff(diff(DD(t, x), x), x)), diff(E(t, x), t) = 0.45e-1*C(t, x)/(1+C(t, x))+0.45e-1*DD(t, x)/(1+DD(t, x))-0.9870e-1*E(t, x)*(diff(diff(E(t, x), x), x)), diff(F(t, x), t) = .7214-.1739837398*F(t, x)*C(t, x)+.1780487805*F(t, x)*DD(t, x)-1.354*F(t, x)*(diff(diff(F(t, x), x), x)), diff(G(t, x), t) = .1739837398*F(t, x)*C(t, x)+.1780487805*F(t, x)*DD(t, x)-1.354*G(t, x)*(diff(diff(G(t, x), x), x))]

(2)

bcs := [(D[2](B))(t, 0) = 0, (D[2](B))(t, 1) = 0, (D[2](C))(t, 0) = 0, (D[2](C))(t, 1) = 0, (D[2](DD))(t, 0) = 0, (D[2](DD))(t, 1) = 0, (D[2](E))(t, 0) = 0, (D[2](E))(t, 1) = 0, (D[2](F))(t, 0) = 0, (D[2](F))(t, 1) = 0, (D[2](G))(t, 0) = 0, (D[2](G))(t, 1) = 0, B(0, x) = 100, C(0, x) = 70, DD(0, x) = 50, E(0, x) = 70, F(0, x) = 100, G(0, x) = 70]

[(D[2](B))(t, 0) = 0, (D[2](B))(t, 1) = 0, (D[2](C))(t, 0) = 0, (D[2](C))(t, 1) = 0, (D[2](DD))(t, 0) = 0, (D[2](DD))(t, 1) = 0, (D[2](E))(t, 0) = 0, (D[2](E))(t, 1) = 0, (D[2](F))(t, 0) = 0, (D[2](F))(t, 1) = 0, (D[2](G))(t, 0) = 0, (D[2](G))(t, 1) = 0, B(0, x) = .100, C(0, x) = .70, DD(0, x) = .50, E(0, x) = .70, F(0, x) = .100, G(0, x) = .70]

(3)

sol := pdsolve(pdes, bcs, numeric);

module () local INFO; export plot, plot3d, animate, value, settings; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; end module

(4)

sol:-plot3d([B(t, x), C(t, x)], t = 0 .. 20, x = 0 .. 20)

Error, (in pdsolve/numeric/plot3d) unable to compute solution for t>HFloat(0.25):
Newton iteration is not converging

 

``


 

Download spatial_1.mw

How to find sgn on maple?

signum.mw

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