论文标题
用于可变系数PDE的紧凑方案的稳定性和鲁棒性的新型差异方程方法
A novel difference equation approach for the stability and robustness of compact schemes for variable coefficient PDEs
论文作者
论文摘要
考虑了可变系数对流扩散方程的四阶精确紧凑型方案。使用基于差异方程的方法得出了完全离散问题的稳定性的充分条件。恒定系数问题被认为是一种特殊情况，并且在理论上证明了紧凑型方案的无条件稳定性。还分析了放大矩阵的条件数，并得出了同一矩阵的估计值。提供了示例以支持确保稳定性的假设。
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.
