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A Second-Order Time Discretization for Second Kind Volterra Integral Equations with Non-Smooth Solutions

Author

Listed:
  • Boya Zhou

    (School of Mathematics and Big Data, Foshan University, Foshan 528225, China)

  • Xiujun Cheng

    (College of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China)

Abstract

In this paper, a novel second-order method based on a change of variable and the symmetrical and repeated quadrature formula is presented for numerical solving second kind Volterra integral equations with non-smooth solutions. Applying the discrete Grönwall inequality with weak singularity, the convergence order O ( N − 2 ) in L ∞ norm is proved, where N refers to the number of time steps. Numerical results are conducted to verify the efficiency and accuracy of the method.

Suggested Citation

  • Boya Zhou & Xiujun Cheng, 2023. "A Second-Order Time Discretization for Second Kind Volterra Integral Equations with Non-Smooth Solutions," Mathematics, MDPI, vol. 11(12), pages 1-10, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2594-:d:1164811
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    References listed on IDEAS

    as
    1. She, Mianfu & Li, Dongfang & Sun, Hai-wei, 2022. "A transformed L1 method for solving the multi-term time-fractional diffusion problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 584-606.
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