Items tagged with pde

hi
I want to solve a pde equation:
 

equa1 := diff(u(x,y), x, x)-y(1+x) = 0;

# with codition:

con:=u(0,y) = 0, (D(u[x]))(0,y) = 0;

the anwer must be :    u(x,y)= y(x2/2  + x3/6)
How can i solve that with maple?

Please excuse my bad English
thanks

I am looking for a numerical solver for a parabolic PDE (up to 2nd order derivatives but no mixed ones) on the spatio-temporal domain [X x Y x T], either as an external package or as MAPLE code.  

I have coded the method of lines on the domain [X x T] and indeed also used pdsolve as a check for that case. However, pdsolve (numerical) cannot solve the PDEs on the domain [X x Y x T].  The run times and memory requirements for the latter case would of course be significantly greater.  

I am about to code up the method of lines (in MAPLE) on the domain [X x Y x T], but am wondering whether there exist external FORTRAN or C code packages that would be faster if called up in MAPLE and whose results would then be post-pocessed in MAPLE.

Does anyone have any suggestions?

MRB

How to find infinitesimals of a system of pdes? I can find out for a single pde but not able able to solve for system of pdes with several dependent and independent variables. Can anyone please provide me the code for that or give some clue. Thanks


Please help me on this :

restart; with(PDETools), with(plots)

n := .3:

Eq1 := (1-n)*(diff(f(x, y), `$`(y, 3)))+(1+x*cot(x))*f(x, y)*(diff(f(x, y), `$`(y, 2)))-(diff(f(x, y), y))/Da+(diff(f(x, y), y))^2+n*We*(diff(f(x, y), `$`(y, 2)))*(diff(f(x, y), `$`(y, 3)))+sin(x)*(theta(x, y)+phi(x, y))/x = x*((diff(f(x, y), y))*(diff(f(x, y), y, x))+(diff(f(x, y), `$`(y, 2)))*(diff(f(x, y), x))):

Eq2 := (diff(theta(x, y), `$`(y, 2)))/Pr+Nt*(diff(theta(x, y), y))^2/Pr+Nb*(diff(phi(x, y), y))*(diff(theta(x, y), y))/Pr+(1+x*cot(x))*f(x, y)*(diff(theta(x, y), y)) = x*((diff(f(x, y), y))*(diff(theta(x, y), x))+(diff(theta(x, y), y))*(diff(f(x, y), x))):

Eq3 := Nb*(diff(phi(x, y), `$`(y, 2)))/(tau*Pr)+Nt*(diff(theta(x, y), `$`(y, 2)))/(tau*Pr)+(1+x*cot(x))*f(x, y)*(diff(phi(x, y), y)) = x*((diff(f(x, y), y))*(diff(phi(x, y), x))+(diff(phi(x, y), y))*(diff(f(x, y), x))):

ValWe := [0, 5, 10]:

bcs := {Nb*(D[2](phi))(x, 0)+Nt*(D[2](theta))(x, 0) = 0, f(0, y) = ((1/12)*y)^2*(6-8*((1/12)*y)+3*((1/12)*y)^2), f(x, 0) = 0, phi(0, y) = -.5*y, phi(x, 12) = 0, theta(0, y) = (1-(1/12)*y)^2, theta(x, 0) = 1, theta(x, 12) = 0, (D[2](f))(x, 0) = Da^(1/2)*(D[2, 2](f))(x, 0)+Da*(D[2, 2, 2](f))(x, 0), (D[2](f))(x, 12) = 0}:

pdsys := {Eq1, Eq2, Eq3}:

p1 := ans[1]:-plot(theta(x, y), x = 1, color = blue):

plots[display]({p1, p2, p3})

 

``


 

Download untitle_2_(1).mw

What's wrong here?

restart; with(PDEtools); PDE2 := diff(u(x, y, t), t$2) = diff(u(x, y, t), x$2)+diff(u(x, y, t), y$2); IBC2s := u(x, 0, t) = 0, u(x, 2, t) = 0, u(0, y, t) = 0, u(4, y, t) = 0, u(x, y, 0) = (.1*(-x^2+4*x))*(-y^2+2*y), (D[3](u))(x, y, 0) = 0; Sol2 := pdsolve({IBC2s, PDE2}); build(Sol2);

Error, invalid input: PDEtools:-build uses a 1st argument, ANS (of type {`=`, PDESolStruc}), which is mis
 

I am wondering if I can use MAPLE to solve PDE set with one initial value problem for "q" and a boundary condition problem for "p". "q" need to be integrated over time, and for each time step, after updating "q", I need to solve poisson equation for "p":

diff(q(x,y,t),t)=-diff(p(x,y,t),x)*diff(q(x,y,t),y)/cos(xy)+diff(p(x,y,t),y)*diff(q(x,y,t),x)/cos(y)+b*cos(y)^2*diff(p(x,y,t),x)+F(x,y)

diff(p(x,y,t),x,x)+diff(p(x,y,t),y,y)+c(y)*p(x,y,t)=q(x,y,t)

IC: q(x,y,0)=q0(x,y)

BC: periodic in x, second type BC in y.

Many Thanks!

Wanying

 

I am trying to see the solution to a PDE that I am coding with initial and boundary conditions. I know with the ODE, it shows the solution, but with the PDE I cannot seem to see it. Any suggestions?

hello,I want to solve a quesstion about heat equation,that the quesstion like this:

I use the code like this

but the results is wrong obviously and what's wrong with this code?

anxious for your help,thanks.

 

 

I can't seem to plot the second derivative graph for f'' versus y. Is it possible to use the fdiff command twice in a line?

Open to all opinions. Any help would be greatly appreciated :)

fyp3.mw

 

Hi all. I need to solve a large number of PDEs (partial differential equations) symbolically and simultaneously, to find the linearly independant answers for all of them, I use

ans := pdsolve({seq(PDE[i]=0,i=1..d)});

The PDEs are all linear first order and it is very easy to solve them one by one by hand, but in some cases I have 100 PDEs or more, so Maple is either very slow or doesn't work. For d=120, it was evaluating for hours without a result.

 

For example I have d=120 PDEs, and 200 variables. It works for d=30 of them (takes 13 minutes on my 16GB RAM  windows 7 computer). So if I do this:

ans1 := pdsolve({seq(PDE[i]=0,i=1..30)});

ans2 := pdsolve({seq(PDE[i]=0,i=31..60)});

ans3 := pdsolve({seq(PDE[i]=0,i=61..90)});

ans4 := pdsolve({seq(PDE[i]=0,i=91..120)});

Then how can I have only one vector of the linearly independent answers of all of them?

 

And in general, is Maple supposed to do this kind of calculations at all?

If yes, do you have any ideas on how to improve this procedure? 

If not, do you know in which software or programming package I can solve a large number of PDEs symbolically?

Your help is much appreciated. 

I'm trying to solve a system that contains the Laplace homogeneous equation and the boundary/initial conditions, thus i'm typing the following code:

> LAPLACE := (D[1, 2](u))(x, y)+(D[2, 2](u))(x, y) = 0;

            D[1, 2](u)(x, y) + D[2, 2](u)(x, y) = 0


> sys[1] := [LAPLACE, u*(x, 0) = 0, u(0, y) = 0, u(1, y) = 0, u(x, 1) = x^2*(1-x)];


[(D[1, 2](u))(x, y)+(D[2, 2](u))(x, y) = 0, u*(x, 0) = 0, u(0, y) = 0, u(1, y) = 0, u(x, 1) = x^2*(1-x)]

but when i use the command pdsolve(sys[1]) the message below appears:

"Error, (in pdsolve/sys/info) ambiguous input: the variables {u} and the functions {u(0, y), u(1, y), u(x, 1), u(x, y)} cannot both appear in the system"
 

So, it seems the declaration of the system isn't correct, but it's exactly how the tutorial of the maplesoft shows it. Could you please make clear what is a system of pde for maple and what is the correct tool for solving a system with boundary/initial conditions?

For the PDE, I can't seem to plot T' as the y-axis, it gives me the error, "Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct". Anyone knows what seem to be the problem? I am open to all ideas and would appreciate any help:)

fyp3.mw

Hi! 

Tried to solve the PDE below (q and p are time-dependent variabels, q(t),p(t)):

pde := diff(rho(t, q, p), t) = -(diff(rho(t, q, p), q))*p+(diff(rho(t, q, p), p))*(2*q+2);
          

pdsolve(pde, rho(t, q, p));
           

And got the answer: 

rho(t, q, p) = _F1(p^2+2*q^2+4*q, -(1/2)*sqrt(2)*arctan((q+1)*sqrt(2)*(1/sqrt(p^2)))+t)

But I'm not sure how to interpret the result. I understand that  _F1 is an arbitrary function, but then I get confused with the comma? I thought that I'd get a function of q and p, where they depend on t. 

Best regards
Sannis

 

Hello! 

For the last couple of days I've been trying really hard to solve the linear PDE 

dR/dt = -dRdH/dqdp + dRdH/(dpdq) . Where R is a function R(t,q(t),p(t)) and H is the hamiltonian H=  p^2/2 +q^2 +2*q .

(dH/dp= p and dH/dq= -2q-2), q and p depends on the time t, and I'm supposed to solve the PDE and then plot the gaussian distribution (2D). 

I tried doing this:

pde := diff(R(t, q1(t), p1(t)), t) = -(diff(R(t, q(t), p(t)), q(t)))*p(t)+(diff(R(t, q(t), p(t)), p(t)))*(-2*q(t)-2)

But pdsolve(pde) gives me:  "Error, (in pdsolve/info) the name of the indeterminate function must be given". 

When I change q(t) to q and p(t) to p I get:

R(t, q, p) = _F1(p^2-2*q^2-4*q, -(1/2)*ln(sqrt(2)*q+p+sqrt(2))*sqrt(2)+t)

And then I'm lost. How do I solve this PDE in maple? 

Thankful for any help 

 

 

with(DifferentialGeometry):with(JetCalculus):
DGsetup([x],[u],E,5);
vars≔x,u,u[1],u[1,1],u[1,1,1];
PDEtools[declare](Q(vars));
TotalDiff(Q(vars),x);
TotalDiff(u[1,1],x);

 

Hi everyone,

Recently I came across the total differentiation command in the PDEtools. For its

documentation, I used the following link

http://www.maplesoft.com/support/help/Maple/view.aspx?path=DifferentialGeometry/JetCalculus/TotalDiff

Unfortunately, when I try to replicate this it did not work as expected. I am getting the total derivative of the expression to be zero. I do not understand where I am going wrong.

You can find my code above. I am also attaching the screen shot of my maple file.

I would really appreciate if someone could help me out. Thanks for your help.


 

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