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

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.