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Exponential Fourier Collocation Methods for First-Order Differential Equations

In: Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations

Author

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  • Xinyuan Wu

    (Nanjing University, Department of Mathematics
    Qufu Normal University, School of Mathematical Sciences)

  • Bin Wang

    (Qufu Normal University, School of Mathematical Sciences)

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.

Suggested Citation

  • Xinyuan Wu & Bin Wang, 2018. "Exponential Fourier Collocation Methods for First-Order Differential Equations," Springer Books, in: Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations, chapter 0, pages 55-84, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-9004-2_3
    DOI: 10.1007/978-981-10-9004-2_3
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