Numerical methods for ordinary differential equations in the 20th century

DOI10.1016/S0377-0427(00)00455-6zbMath0969.65063OpenAlexW2065960630WikidataQ127982900 ScholiaQ127982900MaRDI QIDQ1841941

John C. Butcher

Publication date: 25 September 2001

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

Full work available at URL: https://doi.org/10.1016/s0377-0427(00)00455-6

zbMATH Keywords

stabilityconvergenceinitial value problemshistorical surveyRunge-Kutta methodsEuler methodlinear multistep methodsstiff problemsAdams-Bashforth methodNyström methodMilne methodAdams-Moulton methodHeun method

Mathematics Subject Classification ID

History of mathematics in the 20th century (01A60) Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) History of numerical analysis (65-03)

Related Items (22)

Solving directly special fourth-order ordinary differential equations using Runge-Kutta type method ⋮ A priori error estimation in terms of the third derivative for the method of successive approximations applied to ODE's ⋮ An efficient parallel implementation of explicit multirate Runge-Kutta schemes for discontinuous Galerkin computations ⋮ Estimation of longest stability interval for a kind of explicit linear multistep methods ⋮ Dynamical instability of collapsed dark matter halos ⋮ A new family of multistep numerical integration methods based on Hermite interpolation ⋮ Unnamed Item ⋮ A level-set method for large-scale simulations of three-dimensional flows with moving contact lines ⋮ Approximation, integration and differentiation of time functions using a set of orthogonal hybrid functions (HF) and their application to solution of first order differential equations ⋮ A computational method for solving a problem with parameter for linear systems of integro-differential equations ⋮ Survey on hardware implementation of random number generators on FPGA: theory and experimental analyses ⋮ Direct integrators of Runge-Kutta type for special third-order ordinary differential equations ⋮ Third-order composite Runge–Kutta method for stiff problems ⋮ Numerical solution of third order linear differential equations using generalized one-shot operational matrices in orthogonal hybrid function domain ⋮ Benchmarking numerical methods for lattice equations with the Toda lattice ⋮ Unnamed Item ⋮ A method of solving a nonlinear boundary value problem for the Fredholm integro-differential equation ⋮ Description and analysis of a mathematical model of population growth of \textit{Aedes aegypti} ⋮ Time-domain goal-oriented adaptivity using pseudo-dual error representations ⋮ Explicit integrator of Runge-Kutta type for direct solution of \(u^{(4)} = f(x, u, u', u)\) ⋮ Shifted boundary polynomial corrections for compressible flows: high order on curved domains using linear meshes ⋮ A symmetric nearly preserving general linear method for Hamiltonian problems

Uses Software

• DASSL
• DIFSUB

Cites Work

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