PDE ToolboxThe Partial Differential Equation Toolbox

is a Matlab based collection of tools for solving Partial Differential Equations (PDEs) on a two-dimensional surface using the Finite Element Method (FEM).

The 2-D surface can be drawn using four different types of solid objects: rectangles, ellipses, circles, and polygons.

Start PDE toolbox

Start MATLAB

• Start PDE Toolbox type: >> pdetool

Boundary Value Problem (BVP)Find

PDE in

Under the BC (Boundary Condition)

BC on

u

Ωn u

Ωu

o0

in 1

)1,1()1,1(

Example:

)1,1(

)1,1(

Example of BVP

Find

in

with the BC (Boundary Condition)

on

u u f

0u

(1,1)

3 Steps

I- Define PDE problem

u f

II- Solve the PDE

problem

III- Visualize the results

Setup and Setting

ExampleSolve

u f 0u

I- Define a PDE problem1 – Draw mode: you create the geometry ( set of rectangle, circle, ellipse, and polygon)

2- Boundary mode: specify the boundary conditions

(different types of BC on different boundary segments)

3- PDE mode: specify the type of PDE and the coeff

(Elliptic, Parabolic, Hyperbolic)

II- Solve a PDE problem

1 – Mesh mode: generate and plot meshes ( generate, refine, control parameters, show labels)

2- Solve mode: solve the discrete problem (Elliptic, Parabolic, Hyperbolic)

III- Visualize the results

1 – Plot mode: wide range of visualization possibilities

( color, vector field plots, surface, mesh, contour) ( time-dependent: animated movie)

MATLAB Help (Help/MATLAB Help/Getting Startted/Manipulating Matrices)Read getstart.pdf fileA Matlab tutorial from the University of New Hampshire

Matlab Primer (for an earlier version of Matlab) A Matlab tutorial from the University of New Hampshire MATLAB Online Reference Documentation provides direct hypertext links to specific MATLAB function descriptions (from the Math Dept, University of Florida). Matlab Help Desk (including manuals). Mathworks, Inc., producers of Matlab. Mathtools.net: a technical computing portal for scientific and engineering needs.