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 C0 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].

REFERENCES

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.8 Partial Differential Equations
          Subjects: Elliptic equations

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.8 Partial Differential Equations
          Subjects: Parabolic equations

General Terms:
Algorithms

Keywords:
elliptic parabolic equations, method of lines, spatial discretization methods