Volume 8, Issue 1
A Trilayer Difference Scheme for One-Dimensional Parabolic Systems

Guang-Nan Chen

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J. Comp. Math., 8 (1990), pp. 55-64

Published online: 1990-08

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  • Abstract

In order to obtain the numerical solution for a one-dimensional parabolic system, an unconditionally stable difference method is investigated in [1] If the number of unknown functions is M, for each time step only M times of calculation are needed. The rate of convergence is $O(\tau+h^2)$. On the bais of [1], an alternating calculation difference scheme is preseented in [2]; the rate of the convergence is $O(\tau^2+h^2)$.The difference schemes in [1] and [2] are economic ones. Tor $\alpha-th$ equation, only $U_{\alpha}$ is an unknown function; the others $U_{\beta}$ are given evaluated either in the last step or in the present step. So the practical calculation is quite convenient. The purpose of this paper is to derive a trilayer difference scheme for one-dimensional parabolic systems. it is known that the scheme is also unconditionally stable and the rate of convergence is $O(\tau^2+h^2)$.

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@Article{JCM-8-55, author = {}, title = {A Trilayer Difference Scheme for One-Dimensional Parabolic Systems}, journal = {Journal of Computational Mathematics}, year = {1990}, volume = {8}, number = {1}, pages = {55--64}, abstract = { In order to obtain the numerical solution for a one-dimensional parabolic system, an unconditionally stable difference method is investigated in [1] If the number of unknown functions is M, for each time step only M times of calculation are needed. The rate of convergence is $O(\tau+h^2)$. On the bais of [1], an alternating calculation difference scheme is preseented in [2]; the rate of the convergence is $O(\tau^2+h^2)$.The difference schemes in [1] and [2] are economic ones. Tor $\alpha-th$ equation, only $U_{\alpha}$ is an unknown function; the others $U_{\beta}$ are given evaluated either in the last step or in the present step. So the practical calculation is quite convenient. The purpose of this paper is to derive a trilayer difference scheme for one-dimensional parabolic systems. it is known that the scheme is also unconditionally stable and the rate of convergence is $O(\tau^2+h^2)$. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9419.html} }
TY - JOUR T1 - A Trilayer Difference Scheme for One-Dimensional Parabolic Systems JO - Journal of Computational Mathematics VL - 1 SP - 55 EP - 64 PY - 1990 DA - 1990/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9419.html KW - AB - In order to obtain the numerical solution for a one-dimensional parabolic system, an unconditionally stable difference method is investigated in [1] If the number of unknown functions is M, for each time step only M times of calculation are needed. The rate of convergence is $O(\tau+h^2)$. On the bais of [1], an alternating calculation difference scheme is preseented in [2]; the rate of the convergence is $O(\tau^2+h^2)$.The difference schemes in [1] and [2] are economic ones. Tor $\alpha-th$ equation, only $U_{\alpha}$ is an unknown function; the others $U_{\beta}$ are given evaluated either in the last step or in the present step. So the practical calculation is quite convenient. The purpose of this paper is to derive a trilayer difference scheme for one-dimensional parabolic systems. it is known that the scheme is also unconditionally stable and the rate of convergence is $O(\tau^2+h^2)$.
Guang-Nan Chen. (1970). A Trilayer Difference Scheme for One-Dimensional Parabolic Systems. Journal of Computational Mathematics. 8 (1). 55-64. doi:
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