MATLAB Mathematics - SERC - Index of

5 Differential Equations
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
pdex1
pdex2
pdex3
pdex4
pdex5
Description
Simple PDE that illustrates the straightforward formulation,
computation, and plotting of the solution
Problem that involves discontinuities
Problem that requires computing values of the partial
derivative
System of two PDEs whose solution has boundary layers at
both ends of the interval and changes rapidly for small t
System of PDEs with step functions as initial conditions
Introduction to PDE Problems
pdepe solves systems of parabolic and elliptic PDEs in one spatial variable x
and time t , of the form
c⎛x, t, u,
∂u ------ ⎞ ∂u
------ = x – m ------ ∂ x m f ⎛x, t, u,
∂u ------ ⎞
⎝ ∂x⎠
∂t ∂x ⎝
⎛ ⎝ ∂x⎠⎠
⎞ + s ⎛ x , t , u ,
∂u ------ ⎞
⎝ ∂x⎠
(5-3)
The PDEs hold for t 0 ≤ t ≤ t f and a ≤ x≤ b. The interval [ a,
b]
must be finite.
m can be 0, 1, or 2, corresponding to slab, cylindrical, or spherical symmetry,
respectively. If m > 0 , then a ≥ 0 must also hold.
In Equation 5-3, fxtu∂u ( , , , ⁄ ∂x) is a flux term and sxtu∂u ( , , , ⁄ ∂x)
is a source
term. The flux term must depend on ∂u ⁄ ∂x . The coupling of the partial
derivatives with respect to time is restricted to multiplication by a diagonal
matrix cxtu∂u ( , , , ⁄ ∂x)
. The diagonal elements of this matrix are either
identically zero or positive. An element that is identically zero corresponds to
an elliptic equation and otherwise to a parabolic equation. There must be at
least one parabolic equation. An element of c that corresponds to a parabolic
5-90