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A family of improved Falkner-type methods for oscillatory systems

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  • Li, Jiyong

Abstract

For solving general second-order initial value problems u′′(t)=f(t,u(t),u′(t)), the classical Falkner methods can date back to Falkner’s work in 1936. In this paper, we propose and study a family of improved Falkner-type methods for the oscillatory system u′′(t)+Mu(t)=g(t,u(t)), where g: R × Rd → Rd, in which the first derivative does not appear explicitly, and M ∈ Rd × d is a symmetric positive semi-definite matrix. The new methods take into account the oscillatory structures of the problem and exactly integrate the unperturbed problem u′′(t)+Mu(t)=0. The global error bounds of the new methods are presented. Numerical experiments are performed to show that the new methods are more efficient than other effective methods appeared in the scientific literature.

Suggested Citation

  • Li, Jiyong, 2017. "A family of improved Falkner-type methods for oscillatory systems," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 345-357.
    • Handle: RePEc:eee:apmaco:v:293:y:2017:i:c:p:345-357
    DOI: 10.1016/j.amc.2016.08.046
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    Cited by:

    1. Li, Jiyong, 2021. "Convergence analysis of a symmetric exponential integrator Fourier pseudo-spectral scheme for the Klein–Gordon–Dirac equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 691-713.
    2. Higinio Ramos & Ridwanulahi Abdulganiy & Ruth Olowe & Samuel Jator, 2021. "A Family of Functionally-Fitted Third Derivative Block Falkner Methods for Solving Second-Order Initial-Value Problems with Oscillating Solutions," Mathematics, MDPI, vol. 9(7), pages 1-22, March.

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