Numerical Solution Of Ordinary Differential Equations And Its Application

Much phenomenon in nature and engineering can be described with solution of ordinary differential equation.Many partial differential equations can be translated to ordinary differential equations to find their approximate solution.So,numerical solution of ordinary differential equations is the basis of numerical analyse of differential equations.For it,this article studies on all solutions on existing numerical solution of initial value problem modal of ordinary differential equation.The article mainly discusses some unvarying solution:Eulerian method, echelon method,θ-method, Eulerian method mended, Runge-Kutta method,Adams method etc,stiff equation,and we discuss the symbolic solution of ordinary differential equation.The article summarizes virtue and defect of all kinds of numerical solution through its history and numerical examples.At last,we discuss practicability of some models numerical solution.