Quintic \(C^2\)-spline integration methods for solving second-order ordinary initial value problems

DOI10.1016/S0377-0427(99)00174-0zbMath0974.65073MaRDI QIDQ1971849

Yanyan Li

Publication date: 29 November 2001

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

zbMATH Keywords

numerical resultsabsolute stabilitysplinescollocation methodsnumerical stabilitysecond-order initial value problemsmultistep methodperiodic stabilityfourth order one-step self-starting scheme

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

Related Items (8)

Sixth Order C 2 -Spline Collocation Method for Integrating Second Order Ordinary Initial Value Problems ⋮ Solutions of linear second order initial value problems by using Bernoulli polynomials ⋮ Numerical comparison of methods for solving second-order ordinary initial value problems ⋮ On some 4-point spline collocation methods for solving second-order initial value problems ⋮ Generalized Laguerre pseudospectral method based Laguerre interpolation ⋮ On a class of spline-collocation methods for solving second-order initial-value problems ⋮ Legendre-Gauss collocation method for initial value problems of second order ordinary differential equations ⋮ Computational quartic \(c^3\)-spline and quintic \(c^2\)-spline algorithms for solving second-order initial value problems

Cites Work

• High-order P-stable multistep methods
• Numerov made explicit has better stability
• Multi-step methods are essentially one-step methods
• A note on a diagonally implicit Runge-Kutta-Nyström method
• A two-stage fourth-order ``almost P-stable method for oscillatory problems
• A quartic \(C^ 3\)-spline collocation method for solving second-order initial value problems
• Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
• Numerical Methods for y″ =f(x, y) via Rational Approximations for the Cosine
• Stability of collocation methods for the numerical solution ofy″=f (x,y)
• [https://portal.mardi4nfdi.de/wiki/Publication:4402781 Approximate Solution of the Differential Equation y � � = f(x,y) with Spline Functions]

This page was built for publication: Quintic \(C^2\)-spline integration methods for solving second-order ordinary initial value problems