A four-step trigonometric fitted P-stable Obrechkoff method for periodic initial-value problems

DOI10.1016/j.cam.2005.03.043zbMath1087.65568OpenAlexW1971299028MaRDI QIDQ2576208

Yongming Dai, Zhongcheng Wang, Dongmei Wu

Publication date: 27 December 2005

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

Full work available at URL: https://doi.org/10.1016/j.cam.2005.03.043

zbMATH Keywords

numerical resultsDuffing equationBessel equationP-stablehigh-order derivativetrigonometric fittingsecond-order initial value problem with periodic solutionsfirst-order derivative formulaObrechkoff four-step methodStiefel and Bettis problem

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

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\(P\)-stable Obrechkoff methods of arbitrary order for second-order differential equations ⋮ On the numerical stability of the exponentially fitted methods for first order IVPs ⋮ A new two-step P-stable hybrid Obrechkoff method for the numerical integration of second-order IVPs ⋮ Exponential fitting for interpolation of oscillatory functions. A numerical approach ⋮ Piecewise-linearized methods for initial-value problems with oscillating solutions ⋮ P-stable exponentially-fitted Obrechkoff methods of arbitrary order for second-order differential equations ⋮ P-stable linear symmetric multistep methods for periodic initial-value problems ⋮ Trigonometrically-fitted method with the Fourier frequency spectrum for undamped Duffing equation ⋮ Numerical computation of the coefficients in exponential fitting ⋮ Exponentially-fitted Obrechkoff methods for second-order differential equations ⋮ Trigonometric symmetric boundary value method for oscillating solutions including the sine-Gordon and Poisson equations

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