一类二阶微分方程数值新算法

A New Algorithm for Second Order Differential Equations

通过辛Euler数值算法的构造过程的研究,在发现构造辛Euler法格式的同时,还有另外的两个相似性质的算法格式,对这两种算法格式的研究以及与辛Euler算法的比较,得出数值算法优秀的标准以及优秀数值算法形成过程中需要改进的方向.通过摆方程比较这些数值算法实际的计算效果,得知辛Euler算法格式优于其他两种相似性质的算法格式.

Finds another two similar algorithm formats while constructing symplectic Euler method format through studying the process of symplectic Euler numerical algorithm. Comparing these two formats with symplectic Euler method, finds the standard of an excellent numerical algorithm and the approach of improving such excellent numer- ical algorithm. By pendulum equation compares the numerical algorithms. Proves that the symplectic Euler algorithm format is better than the other two similar algorithm formats.