The numerical analysis of the weighted average method for heat conduction equation in one dimension

Article type: Research Article

Authors: Li, Hongxia

Affiliations: School of mathematics and statistics, Zhejiang University of Finance and Economics, Hangzhou 310018, Zhejiang, China. E-mail: lhx_sh@126.com

Abstract: In this paper, we will consider the weighted average method for heat conduction equation in one dimension. When θ ≠ 1/2 the truncation error of the scheme is O(τ + h^2); if θ = 1/2 the truncation error of the scheme is O(τ ^2 + h^2). When 0 ≤ θ ≤ 1/2, the scheme is stable if and only ifγ ≤ 1/2(1 - 2θ)^{ - 1} and when 1/2 ≤ θ ≤ 1, the scheme is stable for all γ . The numerical experiments are illustrated at the last.

Keywords: Numerical analysis, weighted average method, heat conduction equation

DOI: 10.3233/JCM-150584

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 15, no. 4, pp. 653-661, 2015