Abstract

A numerical solution method based on the reduction of systems of ordinary differential equations to the Shannon form is considered. Shannon’s equations differ in that they contain only multiplication and summation operations. The absence of functional transformations makes it possible to simplify and unify the process of numerical integration of differential equations in the form of Shannon. To do this, it is sufficient in the initial equations given in the normal form of Cauchy to make a simple replacement of variables. In contrast to the classical fourth-order Runge-Kutta method, the numerical method under consideration may have a higher order of accuracy.

中文翻译：

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将其转换为香农形式求解常微分方程的数值方法

摘要

考虑了一种基于将常微分方程组简化为香农形式的数值解法。香农方程式的不同之处在于，它们仅包含乘法和求和运算。无需函数转换，可以简化和统一Shannon形式的微分方程数值积分的过程。为此，以柯西正态形式给出的初始方程式足以对变量进行简单替换。与经典的四阶Runge-Kutta方法相比，所考虑的数值方法可能具有更高的精度。