Abstract
It is very difficult or even impossible to find the exact solution for initial value problem of differential equation . In fact we can only find its approximate solution. So it is important for us to study its numerical solution. For it, this article studies on existing numerical solution of initial value problem of ordinary differential equation. We summarize virtue and defect of all kinds of numerical solution through its history. And we introduce the numerical solution to a given model problem with Eulerian method, Eulerian method mended and R-K method in the environment of Visual C. The source programs and solution are provided, which proves the analysis in theory and provides reference for us to find all kinds of precision reasonable algorithms.
Keywords: Initial value problems of ordinary differential equations; Numerical solution; C language