ABSTRACT
Most physical systems can be described in mathematical terms through differential equations. Instead, solutions can be approximated using numerical methods and in science and engineering, a numeric approximation to the solution is often good enough to solve a problem. This chapter describes the reason for solving differential equations using numerical methods. It explains a numerical solution to a first-order differential equation using Euler– Cauchy method and Runge– Kutta method. A number of other analytical methods of solving differential equations exist. However the differential equations that can be solved by such analytical methods are fairly restricted. Where a differential equation and known boundary conditions are given, an approximate solution may be obtained by applying a numerical method.
