Discretization methods for stable initial value problems

DOI10.1007/BFb0071438zbMath0518.65050OpenAlexW4206112535MaRDI QIDQ1054129

Eckart W. Gekeler

Publication date: 1984

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bfb0071438

zbMATH Keywords

stabilityerror boundsstiff systemsmultistep methodsRunge-Kutta-methods

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Stability and convergence of numerical methods for ordinary differential equations (65L20) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Numerical investigation of stability of solutions to ordinary differential equations (65L07) Method of lines for boundary value problems involving PDEs (65N40)

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On computing smooth solutions of problems with large Lipschitz constants ⋮ Convolution quadrature and discretized operational calculus. I ⋮ What do multistep methods approximate? ⋮ Two concepts for numerical periodic solutions of ODE's ⋮ Difference schemes for solving the Cauchy problem for a second-order operator differential equation ⋮ On the application of mixed finite element methods to the wave equations ⋮ Numerical integration methods in dynamical astronomy ⋮ On the order conditions of Runge-Kutta methods with higher derivatives

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