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Networks and Heterogeneous Media

2024, Volume 19, Issue 2: 740-752. doi: 10.3934/nhm.2024033
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Research article

A second order numerical method for a Volterra integro-differential equation with a weakly singular kernel

  • 1.
    Center for Applied Mathematics of Guangxi, Nanning Normal University, Nanning, 530100, China
  • 2.
    School of Big Data and Artificial Intelligence Chizhou University Chizhou, Anhui 247000, China
  • Received: 27 May 2024 Revised: 05 July 2024 Accepted: 22 July 2024 Published: 24 July 2024

  • In this paper, a second finite difference method on a graded grid is proposed for a Volterra integro-differential equation with a weakly singular kernel. The proposed scheme is obtained by using the two-step backward differentiation formula (BDF2) to discretize the first derivative term and the first-order interpolation scheme to approximate the integral term. The analysis of stability is proved and used to prove the convergence of our presented numerical method in the discrete maximum norm. Finally, Numerical experiments are given to verify the theoretical results.

    Citation: Li-Bin Liu, Limin Ye, Xiaobing Bao, Yong Zhang. A second order numerical method for a Volterra integro-differential equation with a weakly singular kernel[J]. Networks and Heterogeneous Media, 2024, 19(2): 740-752. doi: 10.3934/nhm.2024033

    Related Papers:

  • In this paper, a second finite difference method on a graded grid is proposed for a Volterra integro-differential equation with a weakly singular kernel. The proposed scheme is obtained by using the two-step backward differentiation formula (BDF2) to discretize the first derivative term and the first-order interpolation scheme to approximate the integral term. The analysis of stability is proved and used to prove the convergence of our presented numerical method in the discrete maximum norm. Finally, Numerical experiments are given to verify the theoretical results.



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