Numerical Solution of Differential Equations

Abstract

To study the techniques for solving differential equations based on numerical approximations were developed before programmable computers existed. Differential equations are an important part of many areas of mathematics, from fluid dynamics to celestial mechanics. Many mathematicians have studied the nature of these equations for hundreds of years and there are many well-developed solution techniques. Except for a few special cases, differential equations cannot normally be solved analytically. Instead, there are many numerical methods which have been developed to provide solutions.