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Analysis of Generalized Multistep Collocation Solutions for Oscillatory Volterra Integral Equations

Author

Listed:
  • Hao Chen

    (School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China)

  • Ling Liu

    (School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China)

  • Junjie Ma

    (School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China)

Abstract

In this work, we introduce a class of generalized multistep collocation methods for solving oscillatory Volterra integral equations, and study two kinds of convergence analysis. The error estimate with respect to the stepsize is given based on the interpolation remainder, and the nonclassical convergence analysis with respect to oscillation is developed by investigating the asymptotic property of highly oscillatory integrals. Besides, the linear stability is analyzed with the help of generalized Schur polynomials. Several numerical tests are given to show that the numerical results coincide with our theoretical estimates.

Suggested Citation

  • Hao Chen & Ling Liu & Junjie Ma, 2020. "Analysis of Generalized Multistep Collocation Solutions for Oscillatory Volterra Integral Equations," Mathematics, MDPI, vol. 8(11), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2004-:d:442618
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    Citations

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    Cited by:

    1. Lucas Jódar & Rafael Company, 2022. "Preface to “Mathematical Methods, Modelling and Applications”," Mathematics, MDPI, vol. 10(9), pages 1-2, May.
    2. Jianyu Wang & Chunhua Fang & Guifeng Zhang, 2023. "Multi-Effective Collocation Methods for Solving the Volterra Integral Equation with Highly Oscillatory Fourier Kernels," Mathematics, MDPI, vol. 11(20), pages 1-19, October.

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