Numerical Methods

So far we have seen many methods to solve different types of ODEs and studied the qualitative as well as quantitative behavior of solutions to ODEs. However, the methods available to find solutions and to analyze their behavior are limited; whereas there are uncanny ODEs which arise in the modeling of physical/biological/chemical phenomena. Therefore, many times we have to compromise and be content with an 'approximate solution' or 'numerical solution' to the Cauchy problem/ IVP/ boundary value problem under consideration. In fact, at times we would prefer a numerical solution to an analytical solution.