Numerical solution of ordinary differential equations using mathematical software

Abstract

The differential equation is mathematical tool widely used for description various linear or nonlinear systems and behaviour in the nature not only in the industry. The numerical solution of the differential equation is basic tool of the modelling and simulation procedure. There are various types of numerical methods, the ones described in this contribution comes from the Taylor’s series and big advantage of all of them is in easy programmability or even more some of them are included as a build-in functions in mathematical softwares such as Mathematica or MATLAB. The goal of this contribution is to show how proposed Euler and Runge-Kutta’s methods could be programmed and implemented into MATLAB and examine these methods on various examples. The comparable parameters are accuracy and also speed of the computation.