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.