Solving Differential Equations

Differential equations play a central role in numerics. We introduce basic algorithms for first and second-order initial value problems. This will allow us to numerically solve many interesting problems, for instance, a body falling through the atmosphere, two- and three-body problems, a simple model for galaxy collisions, and the expansion of the Universe. Apart from learning how to deal with numerical errors, mastering multi-dimensional arrays and complex operations are important objectives of this chapter. Moreover, it is shown how to produce histograms and three-dimensional plots.