Numerical Procedure

Abstract

For realistic material functions no analytic solutions are possible, so that one depends all the more on numerical solutions of the basic differential equations. Consequently the activity and the number of results in this field has increased with the numerical capabilities. The growth of computing facilities by leaps and bounds since the 1960s may be illustrated by a remark of M. Schwarzschild (1958): “A person can perform more than twenty integration steps per day”, so that “for a typical single integration consisting of, say, forty steps, less than two days are needed”. The situation has changed drastically since those days when the scientist’s need for meals and sleep was an essential factor in the total computing time for one model. Nowadays one asks rather for the number of solutions produced per second. And these modern solutions are enormously more refined (numerically and physically) than those produced 40 years ago. This progress has been possible because of the introduction of large and fast electronic computers and the simultaneous development of an adequate numerical procedure connected with the name of L.G. Henyey. His method for calculating models in hydrostatic equilibrium is now generally used and will be described later.