Predictor-Corrector Methods for Solving Initial Value Problems

Abstract

Abstract : Numerical solutions of ordinary differential equations (initial value problems) have been given considerable attention, concerning the design and construction of algorithms for their applications in real-life modeling, e.g., modeling of long-range transport of air pollutants in the atmosphere. In this thesis, a new block method of fifth order is derived for solving initial value problems of ordinary differential equations. Several problems from the literature were tested to demonstrate the method's accuracy using the C++ software language. We compare the accuracy of the new block method with the known Runge-Kutta method of the same order