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Method of lines for hyperbolic differential equations. (English) Zbl 0754.65078

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.

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
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