About numerical methods

In computational physics, many mathematical operations have to be carried out numerically. Techniques for doing this are studied in numerical analysis. For a large variety of numerical problems, commercial or public domain software packages are available, and on the whole these are recommended in preference to developing all the numerical software oneself, not only because this saves time but also because available routines are often coded by professionals and hence are hard to surpass in generality and efficiency. To avoid eventual problems with using existing numerical software, it is useful to have some background in numerical analysis. Moreover, knowledge of this field enables you to write codes for special problems for which no routine is available. This chapter reviews some numerical techniques which are often used in computational physics.

There are several ways of obtaining ‘canned’ routines. Commercially available libraries (such as NAG, IMSL) are of very high quality, but often the source code is not available, which might prevent your software from being portable. However, several libraries, such as the ones quoted, are available at many institutes and companies for various types of computers (‘platforms’), so that in practice this restriction is not so severe.

Via the internet, it is possible to obtain a wide variety of public domain routines; a particularly useful site is /www.netlib.org/. Most often these are provided in source code. Another cheap way of obtaining routines is by purchasing a book on numerical algorithms containing listings of source codes and, preferably, a CD (or an internet address) with these sources. A well-known book is Numerical Recipes by Press et al. [1].