The mathematical implications of the design idea of the Runge-Kutta method

摘要

In many cases, it is impossible to find the analytical solutions. In view of the above reasons, it is necessary to study the numerical solution of the initial value problem. This paper will review a numerical solution of the initial value problem for a first-order ordinary differential equation, Runge-Kutta method, the mathematical design behind it. Several questions will be used to illustrate the stability and accuracy of this numerical method.