Sixth Order C 2 -Spline Collocation Method for Integrating Second Order Ordinary Initial Value Problems

DOI10.1080/00207160210956zbMath1024.65070OpenAlexW2032818221MaRDI QIDQ4543524

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Publication date: 6 November 2003

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

Full work available at URL: https://doi.org/10.1080/00207160210956

zbMATH Keywords

convergencesystemsdissipationnumerical experimentsdispersioninitial value problemscollocation methodsspline solutionsspecial second-order equations

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

Related Items (8)

A new approach on the construction of trigonometrically fitted two step hybrid methods ⋮ Symmetric multistep methods with zero phase-lag for periodic initial value problems of second order differential equations ⋮ An optimized two-step hybrid block method for solving general second order initial-value problems ⋮ Solving second order initial value problems by a hybrid multistep method without predictors ⋮ SexticC¹-spline collocation methods for solving delay differential equations ⋮ Trigonometrical fitting conditions for two derivative Runge-Kutta methods ⋮ Efficient adaptive step-size formulation of an optimized two-step hybrid block method for directly solving general second-order initial-value problems ⋮ An efficient optimized adaptive step-size hybrid block method for integrating \(w^{\prime \prime} = F (t, w, w^\prime)\) directly

Cites Work

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• Unconditionally stable methods for second order differential equations
• Runge-Kutta algorithms for oscillatory problems
• A two-stage fourth-order ``almost P-stable method for oscillatory problems
• Quintic \(C^2\)-spline integration methods for solving second-order ordinary initial value problems
• Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
• Two-stage and Three-stage Diagonally Implicit Runge-Kutta Nyström Methods of Orders Three and Four
• Numerical Methods for y″ =f(x, y) via Rational Approximations for the Cosine

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