Mathematics 
MATLAB PDE Solver
This is the MATLAB PDE solver.
PDE InitialBoundary Value Problem Solver  

Solve initialboundary value problems for systems of parabolic and elliptic PDEs in one space variable and time. 
PDE Helper Function
PDE Helper Function  

Evaluate the numerical solution of a PDE using the output of pdepe . 
PDE Examples
These examples illustrate some problems you can solve using the MATLAB PDE solver. Click the example name to see the code in an editor. Type the example name at the command line to run it.
Note
The Differential Equations Examples browser enables you to view the code for the PDE examples, and also run them. Click on the link to invoke the browser, or type odeexamples('pde') at the command line.

Example 
Description 
pdex1 
Simple PDE that illustrates the straightforward formulation, computation, and plotting of the solution 
pdex2 
Problem that involves discontinuities 
pdex3 
Problem that requires computing values of the partial derivative 
pdex4 
System of two PDEs whose solution has boundary layers at both ends of the interval and changes rapidly for small 
pdex5 
System of PDEs with step functions as initial conditions 
Partial Differential Equations  Introduction to PDE Problems 