Functionally-fitted block methods for second order ordinary differential equations

Wu, Jingwen; Tian, Hua

doi:10.1016/j.cpc.2015.08.010

Cited by 3 publications

(1 citation statement)

References 38 publications

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“…Hoang and Sidje [17] presented a class of functionallyfitted Runge-Kutta methods based on separable basis functions and show how to characterize the stability function of the methods in this particular class. Recently, Wu and Tian [46,47] constructed two families of functionally fitted block methods for first and second order ODEs and established the basic theory of the existence and the accuracy of the methods.…”

Section: Jingwen Wu Jintao Hu and Hongjiong Tianmentioning

confidence: 99%

Functionally-fitted block <inline-formula><tex-math id="M1">\begin{document}$ \theta $\end{document}</tex-math></inline-formula>-methods for ordinary differential equations

Wu¹,

Hu²,

Tian³

2020

Discrete &Amp; Continuous Dynamical Systems - S

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We propose a new family of functionally-fitted block θ-methods for numerically solving ordinary differential equations which integrates a chosen set of linearly independent functions exactly. The advantage of such variable coefficient methods is that the basis functions can be chosen to exploit specific properties of the problem that may be known in advance. The basic theory for the proposed methods is established. First, we derive a sufficient condition to ensure the existence of the functionally-fitted block θ-methods, and discuss the independence on integration time for a set of separable basis functions. We then obtain some basic characteristics of the methods by Taylor series expansions, and show that the order of accuracy of r-dimensional functionallyfitted block θ-method is at least r for ordinary differential equations. Numerical experiments are conducted to illustrate the efficiency of the functionally-fitted block θ-methods. 1. Introduction. Consider the following ordinary differential equations (ODEs) y (t) = f (t, y(t)), t ∈ [t 0 , T ], y(t 0) = y 0. (1) Suppose that f : [t 0 , T ] × R → R is continuous and satisfies a Lipschitz condition |f (t, y) − f (t, z)| ≤ L|y − z|, ∀t ∈ [t 0 , T ], y, z ∈ R such that there exists a unique solution. We shall assume that y(t) has continuous derivatives on [t 0 , T ] of any order needed. Numerous classical numerical methods including Runge-Kutta methods, multistep methods and block methods have

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Section: Jingwen Wu Jintao Hu and Hongjiong Tianmentioning

confidence: 99%

Functionally-fitted block <inline-formula><tex-math id="M1">\begin{document}$ \theta $\end{document}</tex-math></inline-formula>-methods for ordinary differential equations

Wu¹,

Hu²,

Tian³

2020

Discrete &Amp; Continuous Dynamical Systems - S

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Block generalized Störmer-Cowell methods applied to second order nonlinear delay differential equations

Zhou

2022

Applied Numerical Mathematics

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Block method for third order ordinary differential equations

Zainuddin

İbrahim

2017

AIP Conference Proceedings

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The problem of third order ordinary differential equations (ODEs) is solved directly by using the block backward differentiation formula. The block method is constructed by utilizing three back values and by differentiating the interpolating polynomial once, twice and thrice. Two approximated solutions are generated concurrently for each integration step. Numerical results indicate the efficiency of the direct method than the usual approach of transforming it into the first order ODEs.

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Functionally-fitted block methods for second order ordinary differential equations

Cited by 3 publications

References 38 publications

Functionally-fitted block <inline-formula><tex-math id="M1">\begin{document}$ \theta $\end{document}</tex-math></inline-formula>-methods for ordinary differential equations

Functionally-fitted block <inline-formula><tex-math id="M1">\begin{document}$ \theta $\end{document}</tex-math></inline-formula>-methods for ordinary differential equations

Block generalized Störmer-Cowell methods applied to second order nonlinear delay differential equations

Block method for third order ordinary differential equations

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