Rational function extrapolation

Abstract

In this thesis, I examine rational function extrapolation to solve the initial value problem in ordinary differential equations. Significant historical achievements leading up to the rational function extrapolation are noted, and a thorough study is made of H. G. Hussel's computer implementation of the method. That Watfiv program is then compared to an Adams Predictor Corrector program over a series of problems with an error tolerance of .0001. The overall results of the computer runs show that although computer costs are at times more expensive, rational function extrapolation is more accurate.