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Linear Multistep Method for Advanced IDEs with Piecewise Constant Arguments

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Listed:
  • Liangcai Mei
  • Boying Wu
  • Yingzhen Lin

Abstract

In this article, based on the linear multistep method, we combined the simplified reproducing kernel method (SRKM) with the optimization method to solve advanced IDEs with piecewise constant arguments. This article also discussed the convergence order and the time complexity of the method. It is proved that the approximate solutions and their derivatives obtained by this algorithm are uniformly convergent. Through two numerical examples, it is proved that the proposed algorithm is obviously better than other methods.

Suggested Citation

  • Liangcai Mei & Boying Wu & Yingzhen Lin, 2022. "Linear Multistep Method for Advanced IDEs with Piecewise Constant Arguments," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:6191276
    DOI: 10.1155/2022/6191276
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    References listed on IDEAS

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    1. Al-Smadi, Mohammed & Arqub, Omar Abu & Shawagfeh, Nabil & Momani, Shaher, 2016. "Numerical investigations for systems of second-order periodic boundary value problems using reproducing kernel method," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 137-148.
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