High algebraic, high phase-lag order embedded Numerov-type methods for oscillatory problems

Authors:
Ch. Tsitouras;T. E. Simos
Affiliations:
Section of Mathematics, General Sciences Department, National Technical University of Athens, Zografou Campus, GR-15780 Athens, Greece;26 Menelaou Street, Amfithea - Paleon Faliron, GR 175 64 Athens, Greece and Section of Mathematics, Department of Civil Engineering, School of Engineering, Democritus University of Thrace, GR-6710 ...
Venue:
Applied Mathematics and Computation
Year:
2002

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Abstract

An embedded Numerov-type method of algebraic order eight with phase-lag orders 10-20 for the numerical integration of second-order periodic initial-value problems is developed in this paper.The method has 10 stages. An error estimation, based on varying the phase-lag order, is introduced and an embedded technique is described. Each method of the embedded pair has a large interval of periodicity. Theoretical evidence and numerical and theoretical results obtained for several well-known problems show the efficiency of the new methods.