Abdulle, Assyr Fourth order Chebyshev methods with recurrence relation. (English) Zbl 1009.65048 SIAM J. Sci. Comput. 23, No. 6, 2041-2054 (2002). 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. Cited in 60 Documents 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 Keywords:stiff ordinary differential equations; explicit Runge-Kutta methods; orthogonal polynomials; parabolic partial differential equations; numerical examples; Chebyshev methods; stability; code ROCK4 Software:RKC PDFBibTeX XMLCite \textit{A. Abdulle}, SIAM J. Sci. Comput. 23, No. 6, 2041--2054 (2002; Zbl 1009.65048) Full Text: DOI