For more than 300 years, physicists have described the motion of masses by rules in the infinitely small: Under the influence of forces, mass elements move by a minute distance in a minute amount of time. Such a description leads to differential equations which to this day are the most important tool of physics. If twice the cause leads to twice the effect, then the equations can usually be solved. In the case of nonlinear differential equations, however, one is often restricted to few solvable special cases or has to resort to numerical solutions. In this chapter, we want to provide an introduction to some of the numerical methods and, in so doing, solve some simple physics examples.
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