Programming a Simple ODE Solver

Ordinary differential equations (ODEs) are widely used in science and engineering, particularly when it comes to modeling dynamic processes. Although analytical methods can be employed to solve simple ODEs, nonlinear ODEs typically require numerical methods for solutions. In this chapter we demonstrate how to program general numerical solvers capable of handling any ODE. Initially we will focus on scalar ODEs, which consist of a single equation and a single unknown. Subsequently, in Section 1.3, we will extend these concepts to systems of coupled ODEs. Acquiring a solid grasp of the concepts presented in this chapter will not only help you with programming your own ODE solvers but also in using a diverse range of readily available, general-purpose ODE solvers in Python or other programming languages.