Hello,

It would be easier to understand and answer with some details on the involved PDEs and ODEs.

How do you tried to solve the PDE part?

Assuming that the PDE parameters are state variables of the ODE part of the model, you just need to discrteize the PDE part in a way to obtain a (maybe huge, it depends on your discretization and system) system of ODE.

regards

Dear Sébastien Gaucel 

thank you for you consideration,my model involves 4 pde which should solve simultaneously,and couple of these partial differential equations involves ode in there coefficients,if i define the ode code according my base parameters (time and X dimension) could i solve it as well?

Thanks alot and waiting for your prompt reply by return.

regards M.Sheikhi

The Matlab function pdepe might be of help. It is applicable to elliptic PDEs.

This function performs basically the task that Sébastien has described. It discretises the PDEs along the spatial dimension with the piecewise nonlinear Galerkin/Petrov-Galerkin

method. This transforms the PDE into a system of ODEs where you have one ODE for each grid point along your spatial dimension. This procedure is often described as the Method of Lines.

Instead of using pdepe, you could also perform the discretisation yourself. The simplest way would be to discretise the spatial derivatives with the finite difference method and to solve the resulting system with one of the inbuilt ODE solvers, e.g. ode45.

Regards,

Daniel