Preface Preface
This is an compact set of Lecture Notes on Numerical Differential Equations. It is divided into three chapters. The first introduces the basics of nowadays' computing environment: Floating Point Systems. The second and the third cover, respectively, numerical methods for Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs). The goal of the book is to be as compact as possible. The book is aimed at making students accustomed with the application of numerical methods and so it focuses more on code implementation than on the theory. Just a few basic theorems are proved in this notes, for the remaining we provide references in case the reader is interested. For each algorithm, we provide editable and runnable MATLAB and/or Python's implementations. For each method we also include code to verify numerically the global order of the method. We also discuss the fundamental concepts of convergence, consistency and stability and illustrate MATLAB's and Python's main ODE's IVP and BVP solvers Roberto De LeoWashington, February 2022