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

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

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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 $O(\tau^2+h^2)$.

• History

Published online: 1990-08

• Keywords