Explicit Runge–Kutta Pairs with One More Derivative Evaluation than the Minimum

DOI10.1137/0914021zbMath0773.65051OpenAlexW1965060499MaRDI QIDQ5286353

E. Smart, Philip W. Sharp

Publication date: 29 June 1993

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0914021

zbMATH Keywords

numerical examplesefficiencystability regionRunge-Kutta pairstruncation coefficientnonstiff initial value problemextra stage

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 (10)

A modified Runge-Kutta method for the numerical solution of ODE's with oscillation solutions ⋮ A general four-parameter non-FSAL embedded Runge-Kutta algorithm of orders 6 and 4 in seven stages ⋮ Design of DIRK schemes with high weak stage order ⋮ A new optimized non-FSAL embedded Runge-Kutta-Nyström algorithm of orders 6 and 4 in six stages ⋮ Parallel implementation of interpolants for Runge-Kutta pairs ⋮ Construction of explicit Runge-Kutta pairs with stiffness detection ⋮ Software based on explicit RK formulas ⋮ An efficient Runge-Kutta \((4,5)\) pair ⋮ Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations ⋮ Embedded (4, 5) pairs of explicit 7-stage Runge-Kutta methods with FSAL property

Uses Software

• NSDTST
• STDTST

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