A fourth algebraic order trigonometrically fitted predictor-corrector scheme for IVPs with oscillating solutions

Authors:
G. Psihoyios;T. E. Simos
Affiliations:
Department of Mathematics and Technology, School of Applied Sciences, Anglia Polytechnic University, East Road, Cambridge CB1 1PT, UK;Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese, GR-22 100 Tripolis, Greece
Venue:
Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
Year:
2005

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Abstract

A scheme of trigonometrically fitted predictor-corrector (P-C) Adams-Bashforth-Moulton methods is constructed in this paper. Our new P-C method is based on the third order Adams-Bashforth scheme (as predictor) and on the fourth order Adams-Moulton scheme (as corrector). We tested the efficiency of our newly developed scheme against well known methods, with excellent results. The numerical experimentation showed that our method is considerably more efficient compared to well known methods used for the numerical solution of initial value problems with oscillating solutions.