Numerical methods for solving the system of differential equations

Abstract

The numerical methods are very useful in estimating the approximate solutions of differential equation’s problems. Among such methods three methods namely Euler’s method, Modified Euler’s method and Runge-Kutta method are studied and are applied to the real life problems to have approximated solutions. Chapter-wise account of this thesis is as follows : Chapter 1 is preliminary in nature. This consists of the basic terminology regarding differential equations and it’s system along with real life examples. Secondly it deals with the origin and applications of differential equations. Chapter 2 deals with the study of numerical methods and their implementation in the problems of differential equations and system of differential equations. It consists of illustration of numerical methods along with examples. Chapter 3 consists of real life problems where differential equations play an important role and for those problems the numerical methods studied in chapter 2 are applied. Two problems naming Pricing policy of goods and R¨ossler system which involves higher order differential equation and system of differential equations respectively are taken. Numerical methods are applied to have approximate solutions. It also consists of matlab implementation for these problems.