论文标题
非线性普通微分方程的精确解
Exact solution of nonlinear ordinary differential equations
论文作者
论文摘要
目前，只有一些特殊的微分方程具有明确的分析解决方案。通常，没有人认为可以在分析上找到非线性方程的精确解决方案。在本文中，基于以下想法，即具有零截断误差的数值方案可以产生精确的解决方案，这是获得非线性普通微分方程初始值问题的精确解决方案的一般公式。同时，此公式使我们能够构建一个具有零截断误差的数值方案，用于求解非线性微分方程。
At present, only some special differential equations have explicit analytical solutions. In general, no one thinks that it is possible to analytically find the exact solution of nonlinear equations. In this article based on the idea that the numerical scheme with zero truncation error can give rise to exact solution, a general formula for the exact solution of the initial value problem of nonlinear ordinary differential equations is obtained. Meanwhile, this formula enables us to construct a numerical scheme with zero truncation error for solving the nonlinear differential equations.
