Dear All,

This's my first post on this website; I'm hoping I can get some useful ideas on how to approach the numerical solution for system of PDE's, with initial and boundary conditions.  I'm using Maple 15.

The PDE is,

pde:={diff(p(r,t),r)-v(r,t)^2/r-g1=0,diff(v(r,t),r$2)+beta*diff(diff(v(r,t),r$2),t)-diff(v(r,t),r)*(1/r)-(beta/r)*diff(diff(v(r,t),r),t) +diff(v(r,t),t)*(beta/r^2)+v(r,t)/r^2+(2/r + C*diff(p(r,t),r))*(diff(v(r,t),r)-v(r,t)/r+beta*diff(diff(v(r,t),r),t)- 1/r * beta*diff(v(r,t),t)-Re*(1+lambda)*exp(1-p(r,t))*diff(v(r,t),t)-(1+lambda)*exp(1-p(r,t))*g2=0};

The initial and boundary conditions are,

IBC:={p(1,t)=k,v(r,0)=0,v(1,t)=sint,v(2,t)=0}

I'm trying to solve and plot,

sol:=pdsolve(pde,IBC,numeric,time=t,range=0..1)

but i'm getting an error; (in pdsolve/numeric/match_pdes_bcs) cannot handle systems with multiple pde describing the time dependence of the same dependent variable or having no time dependence

Regards

J. Lee

As of today it does no longer properly load using Firefox, but using IE works

Good afternoon sir,

I request you to support me with regard to the above cited subject.

@Carl Love

This is the integral

I do it by hand the result is Pi, but I do it with maple VectorCalculus it is zero,

how to do it fairly? please demonstrate.thanks!

Hi folks, I'm running Maple 17.02 and getting very different behaviors from subs and isolate. My actual expressions are way more complicated but this simple example illustrates the problem:

restart; with(PDEtools); F := diff_table(f(x, y, w, z, a, b));

subs(F[x] = Z(x, y, w, z, a, b), F[x]+F[x, b]-10);

subs(F[x] = Z(x, y, w, z, a, b), F[x]+F[x, y]-10);

The last line gives me what I want  Z+Z[y]-10 but the second line gives me Z+F[x,b]-10....

An elementary example of successful using Threads:

Hi all

 
i am solving a system of four coupled differential equations using bvp[midrich]approach..

The code i am using is in the attach files 

command is like

> A1 := dsolve({bc, eq1, eq2, eq3, eq4}, numeric, output = array([seq(0+0.5e-2*i, i = 0 .. 200*bb)]), method = bvp[midrich]);

with(plots)

Hi,

While using pdsolve for a coupled system of pdes, the maple results doen't match with the desired ones.

Here is the system

restart:

Eq1:=diff(f(eta,tau),eta$3)+(f(eta,tau)+h(eta,tau))*diff(f(eta,tau),eta$2)-diff(f(eta,tau),eta$1)^2

+(1+epsilon*cos(Pi*tau))*theta(eta,tau)=Omega*diff(f(eta,tau),tau);

Eq2:=diff(h(eta,tau),eta$3)+(f(eta,tau)+h(eta,tau))*diff(h(eta,tau),eta$2)-diff(h(eta,tau),eta$1)^2

+c*(1+epsilon*cos(Pi*tau...

ASK.zip

Hi all,

In short, I want to use

'ss' expression(1)

to simplify

'kappa' expression (2).

At the moment, I can only archieve it through solving for each variable and get to expression (5).

simplify using siderules failes in this case. Is there another way to do it?

Thanks,

Casper

Hi, 

Struggling to get my head round how to plot the results of the follwoing, as it seems I have 4 variables...

I have a data file containing the results of the following problem:

1) Consider a cube. Each side (a,b,c) has a length of 1 unit.

2) Place an ion (0,0,0) where [a,b and c intersect] and find the associated energy at that point.

3) Move the ion to a point 0.05 units along side a to (0.05,0,0) and re-find the associated energy.

Real application running a very long time in elimination step

z1 := Diff(x1(t),t) = x2(t);

z2 := Diff(x2(t),t) = x3(t);

z3 := Diff(x3(t),t) = x4(t);

z4 := Diff(x4(t),t) = -1*(1.0000*x4(t)-.5109*x3(t)-0.595e-1*x2(t)+3.1086*10^(-15)*(Diff(u(t), t, t, t))-(Diff(u(t), t, t))+.5109*(Diff(u(t), t))+0.595e-1*u(t));

with(Involutive):

with(OreModules):

Alg := DefineOreAlgebra(diff=[D,t], polynom=[t], comm=[a1,a2,a3,u]):

DD := evalm([[D, -1, 0, 0, 0],[0, D, -1, 0, 0],[0, 0, D, -1, 0],[0, -0.0595, -0.5109, D+1, (3.1086*10^(-15))*D^3-D^2+0.5109*D+0.0595]]);

DDtilde := Involution(DD,Alg);

ApplyMatrix(DDtilde, [lambda1(t),lambda2(t),lambda3(t),lambda4(t)],Alg)=evalm([[miu1(t)],[miu2(t)],[miu3(t)],[miu4(t)],[miu(t)]]);

E := Elimination(DDtilde, [lambda1,lambda2,lambda3,lambda4],[miu1,miu2,miu3,miu4,miu],Alg);

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The goal is to get Kalman Form

https://docs.google.com/file/d/0Bxs_ao6uuBDUT25BeVhtWjZwRUU/edit?usp=sharing

https://docs.google.com/file/d/0Bxs_ao6uuBDUVXU5dXh6Rl9zUUU/edit?usp=sharing

I am doing the example in page 707 of Partial Differential control theory Volume 2 by J.F.

when using Robertz Daniel's Ore and Involutive packages

with(Involutive):

with(OreModules):

Alg := DefineOreAlgebra(diff=[D,t...