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Topic: Soving PDE using pdepe
Replies: 7   Last Post: Oct 22, 2013 11:05 AM

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Zuhair

Posts: 9
Registered: 10/18/13
Re: Soving PDE using pdepe
Posted: Oct 18, 2013 11:45 AM
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Yes, I tried it before. When I used the usual form which include the term "r" (growth rate), it is almost the same answer to what I got with the code above. What I do to this model is that I non-dimensionalize the pde first and I get rid of the term r.

But when I non-dimensionalize the differential equations, should I non-dimensionalize the boundary and initial conditions too? Is it correct the way I specify the Neumann boundary conditions for u1 and u2 in the above code?

Thank you.

"Torsten" wrote in message <l3r1c1$7pt$1@newscl01ah.mathworks.com>...
> "Zuhair" wrote in message <l3qnoi$il5$1@newscl01ah.mathworks.com>...
> > Hi
> >
> > I got problem with solving pde using pdepe. Here is my code:
> >
> > % Neumann boundary conditions (bc2.m)
> > function [pl,ql,pr,qr] = bc2(xl,ul,xr,ur,t)
> > pl = [0; 0];
> > ql = [1; 1];
> > pr = [0; 0];
> > qr = [1; 1];
> > ------------------------------------------------------
> > % Initial conditions (initial2.m)
> > function value = initial2(x);
> > value = [0.95*x; 0.05*0.5];
> > --------------------------------------------------------
> > % Equations PDE (eqn2.m)
> > function [c,b,s] = eqn2(x,t,u,DuDx)
> > c = [1; 1]; % coefficiet of time derivatives
> > b = [0.001; 0.001].* DuDx; % diffusion terms
> > s = [u(1)*(1-(u(1)/x)-(1.5)*(u(2)/x));u(2)*(1-(u(2)/0.5)-(1.5)*(u(1)/0.5))]; % Lotka-Volterra 2-species competition model
> > ----------------------------------------------------------------
> > %Solving PDE stored in eqn2.m, bc2.m, and initial2.m
> > close
> > clear
> > clc
> >
> > m = 0;
> > x = linspace(0,1,1000);
> > t = linspace(0,1,10000);
> > sol = pdepe(m,@eqn2,@initial2,@bc2,x,t);
> > u1 = sol(:,:,1);
> > u2 = sol(:,:,2);
> >
> > plot(x,u1(end,:));
> > hold all
> > plot(x,u2(end,:));
> > xlabel('x')
> > ylabel('u(x)')
> >
> > This is the Lotka-Volterra competition model with diffusion term (pde). When I try to solve this model with Neumann boundary conditions, I do not get the correct figure i.e. the correct solution of u1 should look like sigmoid curve which start at 0 (when x=0) and finish at 1 (when x = 1). And the correct solution of u2 also looks like sigmoid curve (but in the opposite direction to u1) and it start at 0.5 (when x = 0) and end at 0 (when x = 1).
> >
> > The initial conditian that should be used is [0.95*x; 0.05*0.5]. And diffusion constant of 0.001.
> >
> > Thanking you in advance for your help.

>
> Did you try what you get when you use the usual form for the source term given under
> http://en.wikipedia.org/wiki/Competitive_Lotka%E2%80%93Volterra_equations
> subtitle "Two species" ?
>
> Best wishes
> Torsten.




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