       Re: Reaction-diffusion PDEs

• To: mathgroup at smc.vnet.net
• Subject: [mg65676] Re: [mg65660] Reaction-diffusion PDEs
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Thu, 13 Apr 2006 02:19:52 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```soln=NDSolve[{
D[u[x,t],t]==0.6u[x,t]-v[x,t]-
u[x,t]^3+0.0002D[u[x,t],{x,2}],
D[v[x,t],t]==1.5u[x,t]-2v[x,t]+
0.01D[v[x,t],{x,2}],
u[x,0]==Sin[2Pi*x],
v[x,0]==Sin[4Pi*x],
u[0,t]==0,v[0,t]==0,
u[1,t]==0,v[1,t]==0},
{u[x,t],v[x,t]},
{x,0,1},{t,0,30},MaxStepSize->0.01][];

Plot3D[Evaluate[u[x,t]/.soln],{x,0,1},{t,0,30}];

Plot3D[Evaluate[v[x,t]/.soln],{x,0,1},{t,0,30}];

Bob Hanlon

>
> From: Skirmantas <skirmantas.janusonis at yale.edu>
To: mathgroup at smc.vnet.net
> Subject: [mg65676] [mg65660] Reaction-diffusion PDEs
>
> Hello,
>
> I'd like to numerically solve the following reaction-diffusion system:
>
> {D[u[x,t],t]==0.6u[x,t]-v[x,t]-u[x,t]^3+0.0002D[u[x,t],x,x], D[v[x,t],t]
==1.5u[x,t]-2v[x,t]+0.01D[v[x,t],x,x], u[x,0]==Sin[2*Pi*x], v[x,0]==Sin
[4*Pi*x]}, where 0<=x<=1, 0<=t<=30, assuming zero-flux boundary
conditions (at x=0 and x=1). I can set up my own discretization and iteration
with the For operator, but I suspect NDSolve may be able to to do it