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Looking at the code of PDEtools:-declare, one sees that it does some brief initializing and then passes the job off to `PDEtools/declare`. I'd like to view this latter procedure, but I can't find it. It is not at the top level, nor is it an export or local of module PDEtools. So where is it?

Hey everybody I am trying to get maple to do some partial differention for me. 

Where 

 

I have PDEtools on but, it doesnt return an expression correctly. It's I think the problem is because Ψ is a function of (x,y) and f is a function of η and η is a function of x and y . U and ν are constants. vand vy are the x and y velocites. 

 

What I would like the program to return when I write 

is something along the lines of 

 

could someone give me a hand on this. I would really apperciate it. 

 

Best Regards, 

Kyle 

I tried using maple to solve the below system of Partial differential equations but itzz not jst coming out... any assistance will be appreciated (post the maple codes if used)

sys2 := -(diff(u(y, t), y, y)) + S*(diff(u(y, t), y)) + diff(u(y, t), t) + M.u(y,t) + (u(y,t)/k)-theta(y,t) = 0,
 -(diff(theta(y, t), y, y))/Pr + diff(theta(y, t), t) + S*(diff(theta(y, t), y)) = 0

The variables are... u(y,t) and theta(y,t)

The initial conditions are;

Analytical PDE solution...

June 25 2013 MPk 5

Hello,

I have found numerous ways of plotting PDEs, but I am trying to ask Maple to calculate the simple analytical solution of one.

Now, Maple is very happy to solve the following with one initial condition:

restart;
with(PDEtools);

pde := diff(u(z, t), t)+c*(diff(u(z, t), z)) = A;
IBC := (u(z, 0) = f(z));

sys:=[pde,IBC];

ans:=pdsolve(sys); 


However, when we take, 
IBC := (u(z, 0) = f(z), D[1](u)(0, t) = 0, D[1](u)(-h, t) = 0);

what am i doing wrong???

> restart;
> with(PDEtools);
> a := 3;
> U := u(r, t);
> wave := a^2*(diff(U, r$2))+(diff(U, r))/r) = diff(U,t$2));
> ics := u(1, t) = 0;
> bcs := diff(U, t) = piecewise(0<= r <b,-2, b<= r<1,0), u(r, 0) = 0;
> s := pdsolve(wave, {bcs, ics});

Error, (in pdsolve/sys) too many arguments; some or all of the following are wrong: [{u(r, t)}, {u(1, t) = 0, u(r, 0) = 0, diff(u(r, t), t) = -2}]

pdetest vs. algsubs...

April 22 2013 Karla 10

Why is there a difference between pdetest and algsubs for a PDE?
Shouldn't pdetest work the same as algsubs for the example below?

restart: with(PDEtools):

Eq:=u(x,t)*diff(u(x,t),t)=0:

tmp:=sin(w*(c*t-x))-(1/4)*epsilon*c^2*cos(w*(c*t+x))^2+epsilon*c^3*w*cos(w*(c*t-x))*sin(w*(c*t-x))*t+(1/4)*epsilon*c^2*cos(w*(c*t-x))^2+(1/8)*c^4*epsilon^2*sin(w*c*t+w*x)+(1/8)*c^4*epsilon^2*sin(w*c*t+w*x)+(1/24)*c^4*epsilon^2*sin(3*w*c*t+3*w*x):

sol:=u(x,t)=tmp:

I have the following problem with the commands "Infinitesimals" and "InvariantSolutions". After using them to a system of firsst-order PDE's, the following message appears:

 

 Error, (in table["k"]) expected a request of prolongation w.r.t one of 2 independent variables; received a request w.r.t the (inexistent) 4th one

Does anybody know, what this message means ? I am a beginner with the commands "Infinitesimals" and "InvariantSolutions"...

Hi in trying to solve these coupled differential equations i get a weird error:

 

> t := diff(X(x), x) = -(1-6*R(x)^(1/2))^(1/2)*x*X(x)/(X(x)*x+R(x))^(1/2), diff(R(x), x) = (1-6*R(x)^(1/2))^(1/2)*x^2*X(x)/(X(x)*x+R(x))^(1/2);
(1/2)
/ (1/2)\
d \1 - 6 R(x) / x X(x)
--- X(x) = - -----------------------------,

 

Hello,

 

 I am getting into the pdetools, in particular the analytical options. I saw that I can test the MAPLE solution to a pde, but I want MAPLE to test my solution,  how could I do that, MAPLE just substitutes my solution into the pde without differentiating and simplifying.

 

Thanks,

 

Daniel

restart:
with(PDEtools):with(plots):
declare(u(x,y,t)):
PDE1:=diff(u(x,y,t),t$1)+a*u(x,y,t)*diff(u(x,y,t),x$1)+diff(u(x,y,t),x$3)+
b*diff(u(x,y,t),y$2)=0;
Sol1:=pdsolve(PDE1);
Test1:=pdetest(Sol1,PDE1);

params:={a=6,b=1,_C1=1,_C2=1,_C3=1,_C4=1};
Sol2:=subs(params,Sol1);
plot3d(subs(t=1,rhs(Sol2)),x=-10..10,y=-10..10,axes=boxed,grid=[50,50],
style=patchnogrid,shading=Z,orientation=[-40,50]);

I converted an ode using the built-in "convert" tool to check some calculations I had done by hand. To my surprise, there was an inconsistency. I converted the ode using PDEtools[dchange], reproducing the steps I had followed manually, and they checked out. So my question is: is there a sign error in convert? (and therefore a bug) or are both conversions correct, and if so are there any lessons to be learned? (is it related to the equation's symmetries?)

Thanks for your comments.

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