A new optimized non-FSAL embedded Runge-Kutta-Nyström algorithm of orders 6 and 4 in six stages

DOI10.1016/S0096-3003(02)00436-8zbMath1032.65073OpenAlexW1989897441MaRDI QIDQ1412423

El-Desouky Rahmo, Moawwad E. A. El-Mikkawy

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)00436-8

zbMATH Keywords

numerical examplesRunge-Kutta-Nyström methodMACSYMAInitial value problemsFSALembedded algorithmRKNStep size control

Mathematics Subject Classification ID

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) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items

Embedded explicit Runge-Kutta type methods for directly solving special third order differential equations \(y = f(x, y)\), Embedded diagonally implicit Runge-Kutta-Nystrom 4(3) pair for solving special second-order IVPs, Nyström methods and singular second-order differential equations, Economical handling of Runge-Kutta-Nyström step rejection, New family for Runge‐Kutta‐Nyström pairs of orders 6(4) with coefficients trained to address oscillatory problems, A trigonometrically adapted 6(4) explicit Runge–Kutta–Nyström pair to solve oscillating systems, Fitted modifications of Runge–Kutta–Nyström pairs of orders 7(5) for addressing oscillatory problems, A family of explicit parallel Runge-Kutta-Nyström methods, A 6(4) optimized embedded Runge-Kutta-Nyström pair for the numerical solution of periodic problems, Unnamed Item, On high order Runge-Kutta-Nyström pairs, Runge-Kutta-Nyström methods of eighth order for addressing linear inhomogeneous problems, Embedded implicit Runge–Kutta Nyström method for solving second-order differential equations, Adaptive multi-step Runge-Kutta-Nyström methods for general second-order ordinary differential equations, Unnamed Item

Uses Software

• MACSYMA

Cites Work

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