基于Grünwald-Letnikov定义改进的短记忆原理方法

Improved short memory principle method based on the Grünwald-Letnikov definition

提出一种改进的短记忆原理方法,即将传统的短记忆原理(short memory principle,SMP)对时间的截断替换为对二项式系数的截断,然后有限数量的二项式系数反复应用于不断倍增的步长,直至覆盖所有先前的时间点。该方法的目的是用小步长保证计算精度,同时用逐渐增大的步长减少计算量。采用带有分数阶阻尼的受迫振动、分数阶非线性Duffing方程和分数阶Lorenz混沌系统为算例说明了该方法的准确性和有效性。

An improved method of the short memory principle was proposed,that is,the truncation of time by the traditional short memory principle(SMP)was replaced by the truncation of binomial coefficients,and then a finite number of binomial coefficients were repeatedly applied to the step size of multiplication until all previous time points were covered.The purpose of the method is to ensure the accuracy of calculation with small step length,and reduce the amount of calculation with gradually increasing step size.The forced vibration with fractional damping,the fractional nonlinear Duffing equationand fractional Lorenz chaos system were used as examples to illustrate the accuracy and effectiveness of the method.