ABSTRACT
This chapter presents some simple differential equations and their analytical solutions. It provides the application of computers, from the software point of view. This survey is not intended to be comprehensive. If the derivatives in any differential system are taken with respect to a single variable, then the system is one of ordinary differential equations. When several independent variables permit the definition of partial derivatives, these would form part of a system of partial differential equations. Numerical methods for the solution of ordinary differential equations of initial value type are usually categorized as single-step or multistep processes. The chapter aims to present powerful, up–to–date, numerical methods for differential equations in a form which is accessible to non–specialists. There exist many software libraries which offer differential equation solvers, in the form of subroutines, to be referenced by users who require the extra flexibility gained from writing their own programs.
