12.4 Partial Differential Equations with pdepe

MATLAB's pdepe solves a class of parabolic/elliptic partial differential equation (PDE) systems. These systems involve a vector-valued unknown function u that depends on a scalar space variable, x, and a scalar time variable, t. The general class to which pdepe applies has the form

where a ? x ? and ? to ?. The integer m can be 0, 1 or 2, corresponding to slab, cylindrical and spherical symmetry, respectively. The function c is a diagonal matrix and the flux and source functions f and s are vector valued. Initial and boundary conditions must be supplied in the following form. For a ? x ? b and t = t ₀ the solution must satisfy u( x, t ₀) = u ₀( x) for a specified function u ₀. For x = a and t ₀ ? t ? t _f the solution must satisfy

for specified functions p _a and q _a. Similarly, for x = b and to ? t ₀ ? t ? t _f,

must hold for specified functions p _b and q _b. Certain other restrictions are placed on the class of problems that can be solved by pdepe; see doc pdepe for details.

A call to pdepe has the general form

  sol =...