Ordinary Differential Equations

Differential equations are the most important mathematical models for describing various physical phenomena. Motion of solid objects or fluid, deformation of elastic objects, heat flow, chemical or nuclear reactions are all modelled by differential equations. If a differential equation has only one independent variable, then it is referred to as an ordinary differential equation. If there are more than one independent variables, then it is called a partial differential equation. Most of the differential equations governing physical phenomena are partial differential equations. However, because of the difficulty in solving them, we often simplify the problem and reduce it to ordinary differential equations. For example, assuming spherical symmetry can reduce a problem in three space variables to that in just one variable. As a result of such simplifications, a large fraction of the differential equations that we come across in practice are ordinary differential equations. However, because of a significant improvement in algorithms for solving partial differential equations and in computing power, the situation is changing.