Comparison of Predictor-Corrector Methods.

The aim of the paper is to provide convenient predictor-corrector P-C methods for obtaining accurate numerical solution at a minimum cost to first order ordinary differential equations ODE. In pursuing this goal, a unified development of the most popular and efficient P-C methods is presented, which includes derivation of formulas and analysis of error propagation and numerical stability. Each method is then coded and programmed using the FORTRAN language. Comparative analysis of the different P-C methods include both theoretical and numerical results. The numerical results were obtained by subjecting each method to a wide variety of test ODE, using a maximum of two corrector applications and a uniform series of step size values. By systematic comparison of the performance of each P-C method the most convenient P-C sets in terms of accuracy and minimum cost are established. Author