Relationship Between Differential Equations and Difference Equation

Abstract

The study of Differential equations and Difference equations play animportant and significant role in many sciences. These equations are used as mathematical tool used in solving various problems in modeling,physics, chemistry,biology, anthropology, etc. or even in social studies. Differential equations are used to solve real life problems by approximation of numerical methods. Theory of Differential and Difference equations has been taught at all levels in high schools and at the universities for all students, including students majoring in Mathematics.

This is a micro –study in which the research is designed in an exploitative, qualitative, descriptive and analytic framework to analyze the differential-difference equations. In this study, theoretical concepts, descriptive, analytical and numerical methods about differential-difference equations which areclarified by related examples. This research article seeks to study the relationship between them.

The finite difference method for solving equations leads to difference equationtheory, developing a parallel between difference equations and differential equations. The first differences are related to the first derivatives. Difference equations are discrete versions of differential equations, and similarly differential equations are continuous versions of difference equations.