The Explicit Method

Abstract

The simplest method of simulating for pdes, and in particular for odes, is the Euler method, in the present context usually called the [explicit method], or EX hereafter. It has many drawbacks (to be outlined) but it does have the advantage of simplicity of programming and if you are willing to let your computer do the hard work, it can yield adequate results in many cases. There are recent examples of the use of the method even for rather complex systems [324, 349] and a textbook on cyclic voltammetry [274] advocates the method (and provides a program in Pascal). One might thus choose the method as such, or choose to use it as a learning tool. The present author prefers the latter. Having learned how to use EX and aware of its drawbacks, one might be ready to learn something more advanced.