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A Trilayer Difference Scheme for One-Dimensional Parabolic Systems

A Trilayer Difference Scheme for One-Dimensional Parabolic Systems

Year:    1990

Journal of Computational Mathematics, Vol. 8 (1990), Iss. 1 : pp. 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(τ+h2). On the basis of [1], an alternating calculation difference scheme is presented in [2]; the rate of the convergence is O(τ2+h2). The difference schemes in [1] and [2] are economic ones. For the α-th equation, only Uα is an unknown function; the others Uβ 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(τ2+h2).

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/1990-JCM-9419

Journal of Computational Mathematics, Vol. 8 (1990), Iss. 1 : pp. 55–64

Published online:    1990-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    10

Keywords: