Trigonometrically fitted predictor: corrector methods for IVPs with oscillating solutions

Authors:
G. Psihoyios;T. E. Simos
Affiliations:
Department of Mathematics, School of Applied Sciences, Anglia Polytechnic University, East Road, Cambridge CB1 1PT, UK;Department of Computer Science & Technology, Faculty of Sciences and Technology, University of Peloponnese, GR-221 00 Tripolis, Greece
Venue:
Journal of Computational and Applied Mathematics - Special issue: Selected papers from the conference on computational and mathematical methods for science and engineering (CMMSE-2002) Alicante University, Spain, 20-25 september 2002
Year:
2003

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Abstract

In this paper we develop a trigonometrically fitted predictor-corrector (P-C) scheme, which is based on the well-known two-step second-order Adams-Bashforth method (as predictor) and on the third-order Adams-Moulton method (as corrector). Numerical experiments show that the new trigonometrically fitted P-C method is substantially more efficient than widely used methods for the numerical solution of initial-value problems (IVPs) with oscillating solutions.