A class of Runge-Kutta formulae of order three and four with reduced evaluations of function

DOI10.1016/S0096-3003(02)00593-3zbMath1032.65077OpenAlexW2025964042MaRDI QIDQ1412537

Xin-Yuan Wu

Publication date: 25 November 2003

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

Full work available at URL: https://doi.org/10.1016/s0096-3003(02)00593-3

zbMATH Keywords

stabilitynumerical experimentsexplicit Runge-Kutta methodExtended Runge-Kutta processesFree-derivative Runge-Kutta processesTwo-step Runge-Kutta 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) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (6)

Two-step Runge-Kutta methods of order over five with reduced function evaluations ⋮ Order conditions for integrators and mappings with applications ⋮ On explicit two-derivative two-step Runge-Kutta methods ⋮ Open formula of Runge-Kutta method for solving autonomous ordinary differential equation ⋮ Accelerated Runge-Kutta methods ⋮ The recursions of order conditions for some Runge-Kutta-like methods

Uses Software

• ATOMFT

Cites Work

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• ATOMFT: Solving ODEs and DAEs using Taylor series
• Runge-Kutta with higher order derivative approximations
• An explicit two-step method exact for the scalar test equation \(y'= \lambda y\)
• Stiffly stable second derivative multistep methods with higher order and improved stability regions
• Some general implicit processes for the numerical solution of differential equations
• The automatic integration of ordinary differential equations
• On the Location of Zeros of Certain Classes of Polynomials with Applications to Numerical Analysis
• Second Derivative Multistep Methods for Stiff Ordinary Differential Equations

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