常微分方程与代数方程求根

Ordinary Differential Equations and the Roots of the Algebraic Equations

讨论了常微分方程与代数方程求根之间的联系。建立了常微分方程的解与代数方程根的一种联系关系,通过这种联系借助于常微分方程的求解,给出以大范围的初值求出代数方程全部实根的一种方法。还讨论了这种方法的几种具体数值求根算法,并对其中的一些有意义的现象进行了分析。

The connection of ordinary differential equation and the roots of the algebraic equations is discussed in this paper. A relationship between solutions of a sort of ordinary differential equations and the roots of the algebraic equations is established, by which all real roots of an algebraic equation using wide initial values can be found via ordinary differential equation solution. Some interesting circumstances of numerical solution of these equations are discussed in detail.