Outline
1- Quick Introduction to MATLAB
2- PDE Toolbox
3- BVP
4- 3 Steps to use PDE Toolbox
5- Worked Example
MATLAB Help (Help/MATLAB Help/Getting
Startted/Manipulating Matrices)
Read getstart.pdf file
A 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.
PDE Toolbox
 The Partial Differential Equation Toolbox is a
Matlab based collection of tools for solving Partial
Differential Equations (PDEs) on a twodimensional 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.
 A brief overview of the major steps of a PDE
Toolbox GUI (pdetool) session:
Start PDE toolbox
 Start MATLAB
 Start PDE Toolbox
type: >> pdetool
Boundary Value Problem (BVP)
 Find
u
PDE
in

 Under the BC (Boundary Condition)
BC
on

Example of BVP
(1,1)
u
u  f
 Find
in

 with the BC (Boundary Condition)
u 0
on

3 Steps
I- Define PDE problem
II- Solve the PDE problem
III- Visualize the results

Setup and Setting

u  f
Example
 Solve
u  f
u 0

I- Define a PDE problem
1 – 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)
Solve A PDE problem