A new twelfth order trigonometrically-fitted Obrechkoff-like method for second order initial value problems

Beny Neta *
Naval Postgraduate School
Department of Applied Mathematics
Monterey, CA 93943
e-mail: bneta@nps.edu, Tel: 1-831-656-2235, Fax: 1-831-656-2355

Received 01/02/2020, Revised 10/12/2020, Accepted 02/03/2021

Abstract: A new trigonometrically-fitted method of order 12 is developed and compared to an existing P-stable method of the same order. Our method fit exactly the sine and cosines functions sin(r?x), cos(r?x), r = 1,2 and monomials up to degree 9. Our method is tested on several linear and nonlinear examples to demonstrate its accuracy and sensitivity to perturbation in the known frequency. We also show where it is preferable to use the trigonometrically-fitted method. Our method shows its efficiency in solving a nonlinear equation both in terms of global accuracy and CPU run time.
c 2021 European Society of Computational Methods in Sciences and Engineering


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