Adams-Bashforth离散算法改进

Improvement of Adams-Bashforth Discrete Algorithm

在函数的Taylor级数展开式中,用差分代替高阶导数,既可避免计算高阶导数,又可提高数值积分的精度。如果只用差分代替2阶导数,则算法为已知的Adams-Bashforth离散算法;如果用差分代替3阶导数,则在不增加算法的复杂度的情况下,提高了算法的精度。从实例计算可知,改进后的Adams-Bashforth算法精度提高了,其精度与3阶Runge-Kutta方法相当。

In expansion formula of Taylor series for a function, difference was substituted for its higher order differential, which can avoid computing the higher order differentials and raised the accuracy of numerical integration. If the difference is substituted for the second order differential, then the algorithm is Adams-Bashforth discrete algorithm. If the difference is substituted for the third differential, then the accuracy is improved without increasing the complexity of algorithm. The calculating example shows the improved Adams-Bashforth algorithm is more accurate, and its accuracy is the same as that of the third Runge-Kutta algorithm.