A Compact Difference Scheme for Multi-point Boundary Value Problems of Heat Equations

doi:10.1007/s42967-019-00025-w

Communications on Applied Mathematics and Computation ›› 2019, Vol. 1 ›› Issue (4): 545-563.doi: 10.1007/s42967-019-00025-w

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A Compact Difference Scheme for Multi-point Boundary Value Problems of Heat Equations

Xuping Wang, Zhizhong Sun

School of Mathematics, Southeast University, Nanjing 210096, China

Received:2018-08-15 Revised:2018-12-14 Online:2019-12-30 Published:2019-10-16
Contact: Zhizhong Sun, Xuping Wang E-mail:zzsun@seu.edu.cn;seuMathWxp@139.com
Supported by:
The research is supported by the National Natural Science Foundation of China (No. 11671081) and the Fundamental Research Funds for the Central Universities (No. 242017K41044).

Abstract

Abstract: In this paper, a compact difference scheme is established for the heat equations with multi-point boundary value conditions. The truncation error of the difference scheme is O(τ² + h⁴), where τ and h are the temporal step size and the spatial step size. A prior estimate of the difference solution in a weighted norm is obtained. The unique solvability, stability and convergence of the difference scheme are proved by the energy method. The theoretical statements for the solution of the difference scheme are supported by numerical examples.

Key words: Heat equation, Multi-point boundary value condition, Compact difference scheme, Energy method

CLC Number:

Xuping Wang, Zhizhong Sun. A Compact Difference Scheme for Multi-point Boundary Value Problems of Heat Equations[J]. Communications on Applied Mathematics and Computation, 2019, 1(4): 545-563.

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References

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A Compact Difference Scheme for Multi-point Boundary Value Problems of Heat Equations

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