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In this paper, a class of two-level difference schemes including a parameter θ are discussed for the numerical solution of one-dimensional telegraphic equations with source terms, where θ∈[0,1]. The truncation errors of these schemes are O (k2 + h4) if θ ≠ 1/3. For θ = 1/3, the accuracy of the present scheme is improved to O(k3 + h4). Numerical results demonstrate the superiority of these present schemes. It is also shown that these schemes are unconditionally stable by the numerical results.