A new high efficient and high accurate Obrechkoff four-step method for the periodic nonlinear undamped Duffing's equation

DOI10.1016/j.cpc.2004.06.090zbMath1196.65124OpenAlexW2021243725MaRDI QIDQ709670

Deying Zhao, Yongming Dai, Zhongcheng Wang, Xiao-Long Song

Publication date: 18 October 2010

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cpc.2004.06.090

zbMATH Keywords

multistep methodhigh-order derivativeObrechkoff methodnumerical solution to the Duffing equationsecond-order initial value problem with periodic solutions

Mathematics Subject Classification ID

Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items (14)

Trigonometrically-fitted multi-derivative linear methods for the resonant state of the Schrödinger equation ⋮ An explicit six-step singularly P-stable Obrechkoff method for the numerical solution of second-order oscillatory initial value problems ⋮ Unnamed Item ⋮ Trigonometrically fitted high-order predictor-corrector method with phase-lag of order infinity for the numerical solution of radial Schrödinger equation ⋮ Symmetric multistep Obrechkoff methods with zero phase-lag for periodic initial value problems of second order differential equations ⋮ A new eight-order symmetric two-step multiderivative method for the numerical solution of second-order IVPs with oscillating solutions ⋮ Trigonometrically fitted two-step Obrechkoff linear methods for the Schrödinger equation ⋮ High phase-lag order trigonometrically fitted two-step Obrechkoff methods for the numerical solution of periodic initial value problems ⋮ Importance of the first-order derivative formula in the Obrechkoff method ⋮ A trigonometrically-fitted one-step method with multi-derivative for the numerical solution to the one-dimensional Schrödinger equation ⋮ P-stable linear symmetric multistep methods for periodic initial-value problems ⋮ Trigonometrically-fitted method with the Fourier frequency spectrum for undamped Duffing equation ⋮ A HIGHLY ACCURATE AND EFFICIENT TRIGONOMETRICALLY-FITTED P-STABLE THREE-STEP METHOD FOR PERIODIC INITIAL-VALUE PROBLEMS ⋮ A four-step trigonometric fitted P-stable Obrechkoff method for periodic initial-value problems

Cites Work

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• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Families of two-step fourth order \(P\)-stable methods for second order differential equations
• A modification of the Stiefel-Bettis method for nonlinearly damped oscillators
• Adaptive methods for periodic initial value problems of second order differential equations
• Stabilization of Cowell's classical finite difference method for numerical integration
• Unconditionally stable methods for second order differential equations
• Obrechkoff versus super-implicit methods for the solution of first- and second-order initial value problems.
• P-Stable Obrechkoff Methods with Minimal Phase-Lag for Periodic Initial Value Problems
• Generalization of the method of slowly varying amplitude and phase to non-linear oscillatory systems with two degrees of freedom
• Symmetric Multistip Methods for Periodic Initial Value Problems
• A P-stable complete in phase Obrechkoff trigonometric fitted method for periodic initial-value problems

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