Algorithm 690: Chebyshev polynomial software for elliptic-parabolic systems of PDEs

Abstract

PDECHEB is a FORTRAN 77 software package that semidiscretizes a wide range of time-dependent partial differential equations in one space variable. The software implements a family of spacial discretization formulas, based on piecewise Chebyshev polynomial expansions with C ⁰ continuity. The package has been designed to be used in conjunction with a general integrator for initial value problems to provide a powerful software tool for the solution of parabolic-elliptic PDEs with coupled differential algebraic equations. Examples are provided to illustrate the use of the package with the DASSL d.a.e integrator of Petzold [18].