Partial Differential Equation Toolbox

Introduction

The objectives of the PDE Toolbox are to provide you with tools that

• Define a PDE problem, e.g., define 2-D regions, boundary conditions, and PDE coefficients.
• Numerically solve the PDE problem, e.g., generate unstructured meshes, discretize the equations, and produce an approximation to the solution.
• Visualize the results.

Can I Use the PDE Toolbox?

The PDE Toolbox is designed for both beginners and advanced users.

The minimal requirement is that you can formulate a PDE problem on paper (draw the domain, write the boundary conditions, and the PDE). Start MATLAB. At the MATLAB command line, type

• pdetool 
  

This invokes the graphical user interface (GUI), which is a self-contained graphical environment for PDE solving. For common applications you can use the specific physical terms rather than abstract coefficients. Using pdetool requires no knowledge of the mathematics behind the PDE, the numerical schemes, or MATLAB. Getting Started guides you through an example step by step.

Advanced applications are also possible by downloading the domain geometry, boundary conditions, and mesh description to the MATLAB workspace. From the command line (or M-files) you can call functions from the toolbox to do the hard work, e.g., generate meshes, discretize your problem, perform interpolation, plot data on unstructured grids, etc., while you retain full control over the global numerical algorithm.

Tutorial

What Problems Can I Solve?