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A second order accurate difference scheme for the heat equation with concentrated capacity

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Summary.

A numerical solution to the one-dimensional heat equation with concentrated capacity is considered. A second-order accurate difference scheme is derived by the method of reduction of order on non-uniform meshes. The solvability, stability and second order L ∞ convergence are proved. A numerical example demonstrates the theoretical results.

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Authors and Affiliations

  1. Department of Applied Mathematics, Southeast University, Nanjing, 210096, Jiangsu Province, P.R. China

    Zhi-zhong Sun

  2. Department of Mathematics, UNC at Charlotte, Charlotte, NC, USA

    You-lan Zhu

Authors
  1. Zhi-zhong Sun
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  2. You-lan Zhu
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Correspondence to Zhi-zhong Sun.

Additional information

Mathematics Subject Classification (2000): Primary 65M06, 65M12, 65M15

The contract grant sponsor: National Natural Science Foundation of CHINA; The contract grant number:19801007

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Sun, Zz., Zhu, Yl. A second order accurate difference scheme for the heat equation with concentrated capacity. Numer. Math. 97, 379–395 (2004). https://doi.org/10.1007/s00211-003-0462-0

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  • DOI: https://doi.org/10.1007/s00211-003-0462-0

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