Adaptive methods for periodic initial value problems of second order differential equations

DOI10.1016/0771-050X(82)90062-6zbMath0479.65044MaRDI QIDQ1162120

U. Anantha Krishnaiah

Publication date: 1982

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

zbMATH Keywords

numerical resultssecond orderperiodic initial value problemsimplicit adaptive methods

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (11)

Obrechkoff methods having additional parameters for general second-order differential equations ⋮ \(P\)-stable Obrechkoff methods of arbitrary order for second-order differential equations ⋮ Additive parameters methods for the numerical integration of \(y=f(t,y,y')\) ⋮ P-stable exponentially-fitted Obrechkoff methods of arbitrary order for second-order differential equations ⋮ Mixed collocation methods for \(y=f(x,y)\) ⋮ A new high efficient and high accurate Obrechkoff four-step method for the periodic nonlinear undamped Duffing's equation ⋮ Importance of the first-order derivative formula in the Obrechkoff method ⋮ A new kind of high-efficient and high-accurate P-stable Obrechkoff three-step method for periodic initial-value problems ⋮ Trigonometrically-fitted method with the Fourier frequency spectrum for undamped Duffing equation ⋮ Exponentially-fitted Obrechkoff methods for second-order differential equations ⋮ A four-step trigonometric fitted P-stable Obrechkoff method for periodic initial-value problems

Cites Work

• P-stable singlestep methods for periodic initial-value problems involving second-order differential equations
• Hybrid numerical methods for periodic initial value problems involving second-order differential equations
• Unconditionally stable methods for second order differential equations
• Numerical integration of products of Fourier and ordinary polynomials
• Stabilization of Cowell's method
• Stability of collocation methods for the numerical solution ofy″=f (x,y)
• Numerical Integrators for Stiff and Highly Oscillatory Differential Equations
• P-stable methods for periodic initial value problems of second order differential equations
• An Averaging Method for the Stiff Highly Oscillatory Problem
• Symmetric Multistip Methods for Periodic Initial Value Problems
• On accuracy and unconditional stability of linear multistep methods for second order differential equations

This page was built for publication: Adaptive methods for periodic initial value problems of second order differential equations