On the method of modified equations. II: Numerical techniques based on the equivalent equation for the Euler forward difference method

DOI10.1016/S0096-3003(98)10030-9zbMath0929.65050OpenAlexW4244788130MaRDI QIDQ1294222

Juan I. Ramos, Francisco R. Villatoro

Publication date: 11 January 2000

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

Full work available at URL: https://doi.org/10.1016/s0096-3003(98)10030-9

zbMATH Keywords

stabilitycomparison of methodsnonlinear systemsRunge-Kutta methodsfinite difference schemesEuler forward methodmodified equation methodssuccessive-correction methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items

Asymptotic analysis of finite difference methods ⋮ A modified equation approach to selecting a nonstandard finite difference scheme applied to the regularized long wave equation ⋮ On the method of modified equations. VI: Asymptotic analysis of and asymptotic successive-corrections techniques for two-point, boundary-value problems in ODE's ⋮ On the method of modified equations. II: Numerical techniques based on the equivalent equation for the Euler forward difference method ⋮ On the method of modified equations. III: Numerical techniques based on the second equivalent equation for the Euler forward difference method ⋮ On the method of modified equations. IV: Numerical techniques based on the modified equation for the Euler forward difference method ⋮ On the method of modified equations. V: Asymptotics analysis of direct-correction and asymptotic successive-correction techniques for the implicit midpoint method

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