On a class of spline-collocation methods for solving second-order initial-value problems

DOI10.1080/00207160701657804zbMath1183.65085OpenAlexW2013612198MaRDI QIDQ3630035

M. Sh. Osman, S. M. Mahmoud

Publication date: 2 June 2009

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

Full work available at URL: http://www.informaworld.com/smpp/./content~db=all~content=a793240575

zbMATH Keywords

convergencecollocation methodabsolute stabilitynumerical exampleserror analysisperiodic solutionsplineinitial value problemphase-laggeneral linear methods

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) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items (9)

Spline collocation method with four parameters for solving a system of fourth-order boundary-value problems ⋮ Solving the telegraph and oscillatory differential equations by a block hybrid trigonometrically fitted algorithm ⋮ A trigonometrically fitted block method for solving oscillatory second-order initial value problems and Hamiltonian systems ⋮ Solving second order initial value problems by a hybrid multistep method without predictors ⋮ An algorithm for second order initial and boundary value problems with an automatic error estimate based on a third derivative method ⋮ High-order continuous third derivative formulas with block extensions fory″=f(x, y, y′) ⋮ Functionally fitted block method for solving the general oscillatory second-order initial value problems and hyperbolic partial differential equations ⋮ Implicit third derivative Runge-Kutta-Nyström method with trigonometric coefficients ⋮ Third derivative modification of \(k\)-step block Falkner methods for the numerical solution of second order initial-value problems

Uses Software

• Mathematica

Cites Work

• Unnamed Item
• Stabilization of Cowell's classical finite difference method for numerical integration
• Quintic \(C^2\)-spline integration methods for solving second-order ordinary initial value problems
• A new sixth-order algorithm for general second order ordinary differential equations
• Solving Ordinary Differential Equations I
• 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)
• On some 4-point spline collocation methods for solving second-order initial value problems

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