Volume 1, Issue 2
Two Algorithms for Solving a Kind of Heat Conduction Equations

Cheng-Pu Tong & Xu-Ming Chen

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J. Comp. Math., 1 (1983), pp. 106-115

Published online: 1983-01

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  • Abstract

In this paper, a strategy is suggested for numerical solution of a kind of parabolio partial differential equations with nonlinear boundary conditions and discontinuous coefficients, which arise from practical engineering problems. First, a difference equation at the discontinuous point is established in which both the stability and the truncation error are consistent with the total difference equations. Then, on account of the fact that the coefficient matrix of the difference equations is trigiagonal and nonlinearity appears only in the first and the last equations, two algorithms are suggested: a mixed method combining the modified Gaussian elimination method with the successive recursion method, and a variant of the modified Gaussian elimination method. These algorithms are shown to be effective.

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@Article{JCM-1-106, author = {Cheng-Pu Tong and Xu-Ming Chen}, title = {Two Algorithms for Solving a Kind of Heat Conduction Equations}, journal = {Journal of Computational Mathematics}, year = {1983}, volume = {1}, number = {2}, pages = {106--115}, abstract = { In this paper, a strategy is suggested for numerical solution of a kind of parabolio partial differential equations with nonlinear boundary conditions and discontinuous coefficients, which arise from practical engineering problems. First, a difference equation at the discontinuous point is established in which both the stability and the truncation error are consistent with the total difference equations. Then, on account of the fact that the coefficient matrix of the difference equations is trigiagonal and nonlinearity appears only in the first and the last equations, two algorithms are suggested: a mixed method combining the modified Gaussian elimination method with the successive recursion method, and a variant of the modified Gaussian elimination method. These algorithms are shown to be effective. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9687.html} }
TY - JOUR T1 - Two Algorithms for Solving a Kind of Heat Conduction Equations AU - Cheng-Pu Tong & Xu-Ming Chen JO - Journal of Computational Mathematics VL - 2 SP - 106 EP - 115 PY - 1983 DA - 1983/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9687.html KW - AB - In this paper, a strategy is suggested for numerical solution of a kind of parabolio partial differential equations with nonlinear boundary conditions and discontinuous coefficients, which arise from practical engineering problems. First, a difference equation at the discontinuous point is established in which both the stability and the truncation error are consistent with the total difference equations. Then, on account of the fact that the coefficient matrix of the difference equations is trigiagonal and nonlinearity appears only in the first and the last equations, two algorithms are suggested: a mixed method combining the modified Gaussian elimination method with the successive recursion method, and a variant of the modified Gaussian elimination method. These algorithms are shown to be effective.
Cheng-Pu Tong & Xu-Ming Chen. (1970). Two Algorithms for Solving a Kind of Heat Conduction Equations. Journal of Computational Mathematics. 1 (2). 106-115. doi:
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