An Overview of Numerical and Analytical Methods for Solving Ordinary Differential Equations

Mathematics

Differential Equations are among the most important Mathematical tools used in creating models in the science, engineering, economics, mathematics, physics, aeronautics, astronomy, dynamics, biology, chemistry, medicine, environmental sciences, social sciences, banking and many other areas A differential equation that has only one independent variable is called an Ordinary Differential Equation (ODE), and all derivatives in it are taken with respect to that variable. Most often, the variable is time, t; although, I will use x in this paper as the independent variable. The differential equation where the unknown function depends on two or more variables is referred to as Partial Differential Equations (PDE). In this paper, researcher presents the basic and commonly used numerical and analytical methods of solving ordinary differential equations. The results of these efforts are shown in the last sections of this chapter. We present theorems describing the existence and uniqueness of solutions to a wide class of first order differential equations.

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