Next Article in Journal
Comparative Analysis of Machine Learning Models for Prediction of Remaining Service Life of Flexible Pavement
Next Article in Special Issue
Mixed Generalized Multiscale Finite Element Method for Darcy-Forchheimer Model
Previous Article in Journal
On Inverses of the Dirac Comb
Previous Article in Special Issue
Scattered Data Interpolation and Approximation with Truncated Exponential Radial Basis Function
Open AccessReview

Trigonometrically-Fitted Methods: A Review

by Changbum Chun 1 and Beny Neta 2,*
1
Department of Mathematics, Sungkyunkwan University, Suwon 16419, Korea
2
Naval Postgraduate School, Department of Applied Mathematics, Monterey, CA 93943, USA
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1197; https://doi.org/10.3390/math7121197
Received: 28 October 2019 / Revised: 27 November 2019 / Accepted: 2 December 2019 / Published: 6 December 2019
(This article belongs to the Special Issue Computational Mathematics, Algorithms, and Data Processing)
Numerical methods for the solution of ordinary differential equations are based on polynomial interpolation. In 1952, Brock and Murray have suggested exponentials for the case that the solution is known to be of exponential type. In 1961, Gautschi came up with the idea of using information on the frequency of a solution to modify linear multistep methods by allowing the coefficients to depend on the frequency. Thus the methods integrate exactly appropriate trigonometric polynomials. This was done for both first order systems and second order initial value problems. Gautschi concluded that “the error reduction is not very substantial unless” the frequency estimate is close enough. As a result, no other work was done in this direction until 1984 when Neta and Ford showed that “Nyström’s and Milne-Simpson’s type methods for systems of first order initial value problems are not sensitive to changes in frequency”. This opened the flood gates and since then there have been many papers on the subject. View Full-Text
Keywords: second order initial value problems; linear multistep methods; Obrechkoff schemes; trigonometrically fitted second order initial value problems; linear multistep methods; Obrechkoff schemes; trigonometrically fitted
MDPI and ACS Style

Chun, C.; Neta, B. Trigonometrically-Fitted Methods: A Review. Mathematics 2019, 7, 1197.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop