Symbolic derivation of Runge-Kutta methods

DOI10.1006/jsco.1994.1048zbMath0819.65108OpenAlexW2122336811MaRDI QIDQ1346482

Mark Sofroniou

Publication date: 4 April 1995

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jsco.1994.1048

zbMATH Keywords

complexityGröbner basescomputer algebraRunge-Kutta methodsorder conditionssymbolic Mathematica package Butcher.m

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Nonlinear ordinary differential equations and systems (34A34) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Complexity and performance of numerical algorithms (65Y20)

Related Items (8)

Optimal four-stage symplectic integrators for molecular dynamics problems ⋮ Symbolic derivation of Runge-Kutta order conditions ⋮ Symbolic derivation of order conditions for hybrid Numerov-type methods solving \(y^{\prime\prime} =f(x,y)\) ⋮ Unnamed Item ⋮ Construction of explicit Runge-Kutta pairs with stiffness detection ⋮ Runge-Kutta methods for quadratic ordinary differential equations ⋮ Symbolic derivation of Runge-Kutta-Nyström order conditions ⋮ Order bound for a family of parallel Runge-Kutta-Nyström methods through computer algebra

Uses Software

• Mathematica
• butcher

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