Algorithms and implementations

Avast amount of computer models are based on ordinary and partial differential equations. This book is an introduction to the various scientific ingredients we need for reliable computing with such type of models. Akey theme is to solve differential equations numerically on acomputer. Many methods are available for this purpose, but the focus here is on finite difference methods, because these are simple, yet versatile, for solving awide range of ordinary and partial differential equations. The present chapter first presents the mathematical ideas of finite difference methods and derives algorithms, i.e., formulations of the methods ready for computer programming. Then we create programs and learn how we can be sure that the programs really work correctly. © The Author(s) 2016.