Abstract
Practically, the engineer’s deal with a lot of problems that can be expressed
mathematically by ordinary differential equations (ODEs). These ODEs can be solved
using both direct and iterative methods. The latter is popular as, in this case, the
solution techniques are based only on the basic arithmetic operations. In this chapter,
at first, we studied ordinary differential equations. Secondly, fundamental theories for
the solutions of these differential equations are discussed. Then, various numerical
solution techniques are explained in this regard. At the end of each technique,
solutions to various engineering problems are discussed.
Keywords: Ordinary differential equation, Taylor series method, Picard’s method, Euler’s method, Runge-Kutta Finite difference formulae, Predictor-Corrector method, solving simultaneous first order ODEs, solving higher order ODEs.