Numerical Solution Of Ordinary Differential Equations And Its Application

Initial value problem model of differential equation is a kind of familiar mathematical model on Mathematical Contest in Modeling .Some simple and typical model of differential equation can acquire its exact solution for example linear equation , a certain special first order nonlinear equation etc. and can be utilized on theoretic result .but we often come into contact with initial value problem model and it is very difficult or even impossible to find its exact solution, in fact we can only find its approximate solution . So it is important for us to study its numerical solution and require its numerical solution. For it, this article studies on all solutions on existing numerical solution of initial value problem model of ordinary differential equation. The article mainly discusses the precision of model of ordinary differential equation of many kinds numerical solution frequently-used numerical solution: Eulerian method, Eulerian method backwards, -method, Eulerian method mended, R-K method, Adams extrapolation formula, Adams interpolation formula etc .The article summarizes virtue and defect of all kinds of numerical solution through its history and numerical examples, It provides reference for modeling for all kinds of precision reasonable solution mathematical model and mathematical contest .At last, we give similar and typical examples on numerical solution of differential equation model ,such as distribution model of consuming durables, numerical solution of motorman potation motoring for fend model etc. It discusses practicability of three models numerical solution.