Exponential Fourier Collocation Methods for First-Order Differential Equations

Xinyuan Wu () and Bin Wang
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Xinyuan Wu: Nanjing University, Department of Mathematics
Bin Wang: Qufu Normal University, School of Mathematical Sciences

Chapter Chapter 3 in Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations, 2018, pp 55-84 from Springer

Abstract: Abstract CommencingExponential Fourier collocation methods from the variation-of-constants formula and incorporating a local Fourier expansion of the underlying problem with collocation methods, this chapter presents a novel class of exponential Fourier collocation methods (EFCMs) for solving systems of first-order ordinary differential equations. We discuss in detail the connections of EFCMs with trigonometric Fourier collocation methods (TFCMs), the well-known Hamiltonian Boundary Value Methods (HBVMs), Gauss methods and Radau IIA methods. It turns out that the novel EFCMs are an extension, in a strict mathematical sense, of these existing methods in the literature.

Keywords: Fourier Collocation Method; Local Fourier Expansion; Gauss Method; First-order Ordinary Differential Equations; Algebraic Order (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-9004-2_3

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DOI: 10.1007/978-981-10-9004-2_3

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