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Fully discretized methods based on boundary value methods for solving diffusion equations

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  • Zhao, Jingjun
  • Jiang, Xingzhou
  • Xu, Yang

Abstract

Based on boundary value methods, we establish a kind of new fully discretized methods for solving one-dimensional diffusion equations. The proposed methods are composed of a series of full discretizations with multi-time-level and multi-space-level. For the full discretizations, we give the local truncation error. Moreover, we analyze the stability of the proposed methods and obtain the corresponding error estimate. Meanwhile, we make some numerical experiments to show that the proposed methods are stable and own high accuracy.

Suggested Citation

  • Zhao, Jingjun & Jiang, Xingzhou & Xu, Yang, 2022. "Fully discretized methods based on boundary value methods for solving diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    • Handle: RePEc:eee:apmaco:v:418:y:2022:i:c:s0096300321009310
    DOI: 10.1016/j.amc.2021.126848
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    References listed on IDEAS

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    1. Manni, Carla & Mazzia, Francesca & Sestini, Alessandra & Speleers, Hendrik, 2015. "BS2 methods for semi-linear second order boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 255(C), pages 147-156.
    2. Wang, Huiru & Zhang, Chengjian & Zhou, Yongtao, 2018. "A class of compact boundary value methods applied to semi-linear reaction–diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 69-81.
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