本文把在不稳定导热问题中常见的一维抛物型微分方程转化为对时间为唯一变量的常系数线性微分方程组。然后对该方程组从τ—τ+Δτ求解,从而建立了差分方程组。通过实例计算表明,此法使计算速度有所提高,精度也能满足要求。文中还提出了简单的物理解释。并指出将此法推广至二维、三维问题的可能性。 In this paper, the one-dimensional parabolic differential equation which is common in the problem of unstable thermal conductivity is transformed into a system of linear differential equations with constant coefficients which is the only variable in time. Then, the system of equations is solved from τ-τ + Δτ to establish the system of difference equations. The example shows that this method can improve the calculation speed and the precision can meet the requirement. The article also proposed a simple physical explanation. And points out the possibility of extending this method to two-dimensional and three-dimensional problems.