How to solve with Matlab a PDE with periodical boundary conditions.

Dear,

I would like to solve the following PDE for the function u(x,t):

Du/Dt = (ia - 1)u + i([u]^2)u - ib(D²u/Dx²) + F

where i = sqrt(-1) and a,b,F are real quantities, known. And with the periodic boundary condition: u(x,t) = u(x+A,t) , being A the period. And a initial condition u(x,0) = f(x). With A and f(x) also known.

So far I couldn't find a function in Matlab to do so. I tried pdepe but it seems I cannot implement periodic boundary conditions.

What would be the best option to solve such PDE in Matlab?

Thanks alot for the help. Pablo

Answer 1

[Torsten]

Discretize your PDE in space and solve the resulting System of ordinary differential equations using ODE15s (method-of-lines approach).

Best wishes

Torsten.

[Maulik Shah]

Hi Torsten, I have a fourth order PDE with periodic boundary conditions. I have discretized such an equation using central difference schemes in FDM. However, it gives me a 7 point stencil. As a result, I need 6 "guard" points. Do I also include equation for these 6 extra points in the function that is being solved using ode15s?