Kreiss, Heinz-Otto; Scherer, Godela Method of lines for hyperbolic differential equations. (English) Zbl 0754.65078 SIAM J. Numer. Anal. 29, No. 3, 640-646 (1992). Runge-Kutta methods are used in the method of lines approach to solve hyperbolic partial differential equations. Conditions that they are locally stable are derived. Reviewer: P.Y.Yalamov (Russe) Cited in 10 Documents MSC: 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 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 35L45 Initial value problems for first-order hyperbolic systems Keywords:stiff ordinary differential equation; stability region; Runge-Kutta methods; method of lines PDFBibTeX XMLCite \textit{H.-O. Kreiss} and \textit{G. Scherer}, SIAM J. Numer. Anal. 29, No. 3, 640--646 (1992; Zbl 0754.65078) Full Text: DOI