Collocation Runge–Kutta–Nyström methods for solving second-order initial value problems

DOI10.1080/00207160.2021.1900567zbMath1480.65167OpenAlexW3135552027MaRDI QIDQ5033397

Nguyen Si Hoang

Publication date: 22 February 2022

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2021.1900567

zbMATH Keywords

superconvergencecollocationRunge-Kutta-Nyströmsecond-order IVP

Mathematics Subject Classification ID

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) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60)

Related Items (2)

An adaptive one-point second-derivative Lobatto-type hybrid method for solving efficiently differential systems ⋮ Explicit Runge-Kutta-Nyström methods for the numerical solution of second order linear inhomogeneous IVPs

Uses Software

• Matlab
• RODAS

Cites Work

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• Numerical experiments with some explicit pseudo two-step RK methods on a shared memory computer
• Note on the performance of direct and indirect Runge-Kutta-Nyström methods
• Variable stepsize implementation of multistep methods for \(y\prime\prime =f(x,y,y^{\prime})\)
• Continuous parallel-iterated RKN-type PC methods for nonstiff IVPs
• Stability of collocation methods for the numerical solution ofy″=f (x,y)
• Semiexplicit A-Stable Runge-Kutta Methods
• Spectral Methods in MATLAB
• Explicit pseudo two-step runge-kutta methods for parallel computers^∗
• Numerical Methods for Ordinary Differential Equations
• Mixed collocation methods for \(y=f(x,y)\)

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