How to solve second order partial differential equations ?

I have set of equations which I need to solve using pdetool. I am attaching snapshot of equations. How can I solve these ?

Answer 1

[Bill Greene]

This problem is straightforward to solve using PDE Toolbox. I suggest you look at this example http://www.mathworks.com/help/pde/examples/heat-distribution-in-a-circular-cylindrical-rod.html for how to handle cylindrical geometry and this example for how to handle multiple layers http://www.mathworks.com/help/pde/examples/deflection-of-a-piezoelectric-actuator.html

You don't show any boundary conditions on the edges where x=constant. If those edges are insulated (i.e. your problem is really one-dimensional), you can use the pdepe function in core MATLAB. pdepe has an option to "automatically" handle the cylindrical coordinate system so it is particularly easy to use for this problem.

Bill

Answer 2

[Torsten]

This is a multilayer problem with internal heat sources.

As far as I know, there is no ready-to-use pdetool to solve this kind of problem.

You will have to discretize your equations, boundary conditions and transition conditions between the layers in space and solve the resulting system of ordinary differential equations in time by an ODE integrator (ODE15s).

Best wishes

Torsten.