In this chapter we introduce several algorithms to solve numerically Initial Value Problems (IVPs) and Boundary Value Problems (BVPs) in the setting of Ordinary Differential Equations (ODEs). Each algorithm is presented in its one-dimensional version except for a few examples of systems in the plane solved with variants of the Euler method. Finally, we also illustrate some basic SciPy and MATLAB IVP and BVP solvers. We provide links to further readings in several "asides" throughout the book, like the one in this page.
