Fourth-order accurate compact schemes for variable coefficient convection diffusion equations are considered. A sufficient condition for the stability of the fully discrete problem is derived using a difference equation based approach. The constant coefficient problems are considered as a special case, and the unconditional stability of compact schemes for such case is proved theoretically. The condition number of the amplification matrix is also analyzed, and an estimate for the same is derived. The examples are provided to support the assumption taken to assure stability.

翻译：针对变系数对流扩散方程的四阶精度紧致格式展开研究. 采用基于差分方程的方法, 推导了全离散问题稳定性的充分条件. 将常系数问题作为特例考虑, 理论上证明了此类情形下紧致格式的无条件稳定性. 分析了放大矩阵的条件数并给出了其估计式. 提供了数值算例以支撑确保稳定性所采用的假设条件.