@Article{JCM-8-55,
author = {Guang-Nan Chen},
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}
}