Stepsize restrictions for stability in the numerical solution of ordinary and partial differential equations

DOI10.1016/0377-0427(87)90124-5zbMath0633.65065OpenAlexW2037695239MaRDI QIDQ1096345

H. W. J. Lenferink, J. F. B. M. Kraaijevanger, Marc N. Spijker

Publication date: 1987

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(87)90124-5

zbMATH Keywords

stabilitystiff ordinary differential equationsRosenbrock methodsRunge-Kutta methodsone-step methodmaximum normcontractivityexpository paperlinear, time-dependent systems

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) 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) Numerical methods for initial value problems involving ordinary differential equations (65L05) Initial value problems for linear higher-order PDEs (35G10) Higher-order parabolic equations (35K25)

Related Items (11)

Stability analysis of a Galerkin/Runge-Kutta Navier-Stokes discretisation on unstructured tetrahedral grids ⋮ A selected method for the optimal parameters of the AOR iteration ⋮ Stability radius of polynomials occurring in the numerical solution of initial value problems ⋮ Numerical solution of two asset jump diffusion models for option valuation ⋮ Contractivity of Runge-Kutta methods ⋮ Maximum norm contractivity of discretization schemes for the heat equation ⋮ Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations ⋮ Stability analysis of preconditioned approximations of the Euler equations on unstructured meshes ⋮ On resolvent conditions and stability estimates ⋮ Stability of the method of lines ⋮ Stability and boundedness in the numerical solution of initial value problems

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