Basic Numerical Methods for Ordinary Differential Equations
As you probably know or have heard of, differential equations are everywhere. A typical example is the law of Newton mechanics or evolution equations arising in biology.
Differential equations is a huge and active field in mathematics and this article aims by no means to introduce into this field. My intention is rather to give an overview of methods and ideas used for solving ordinary differential equations numerically.
So if you already use solvers as provided in various libraries, you may find it interesting to understand in a little more detail on which ideas they are built on. We restrict ourselves to two very common used methods, which I think, show very nicely the general concepts and problems.
An example of such a system is (Lorenz-system):
For what follows we assume that the given initial value problem has a unique solution. For…
