×

Fourth order Chebyshev methods with recurrence relation. (English) Zbl 1009.65048

Summary: A new family of fourth order Chebyshev methods (also called stabilized methods) is constructed. These methods possess nearly optimal stability regions along the negative real axis and a three-term recurrence relation. The stability properties and the high order make them suitable for large stiff problems, often space discretization of parabolic partial differential equations. A new code ROCK4 is proposed, illustrated at several examples, and compared to existing programs.

MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
35K55 Nonlinear parabolic equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65Y15 Packaged methods for numerical algorithms

Software:

RKC
PDFBibTeX XMLCite
Full Text: DOI