协调多时次差分格式及其稳定性

A harmonized multi-time difference scheme and its stability

提出对求解常微分方程的各种数值算法,可以建立与之相协调的多时次差分格式.并从数学上给出了一个其计算稳定性的充分条件,同时提出了一种改进的最小二乘法来拟合自忆系数,以期在实际计算过程中既可以改善计算效果,同时也可使其稳定性得以保障.

In this paper, a harmonized multi-time difference scheme is established, which can be easily constructed on any numerical difference scheme of ordinary differential equations. A sufficiently stable condition is proved in mathematics. If the memorial coefficients determined by an improved method of least square, it is expected that this new scheme can integrate stably in a longer period, and a better result can be achieved.