Translator Disclaimer
2018 Exponentially Fitted and Trigonometrically Fitted Explicit Modified Runge-Kutta Type Methods for Solving y x = f x , y , y
N. Ghawadri, N. Senu, F. Ismail, Z. B. Ibrahim
J. Appl. Math. 2018: 1-19 (2018). DOI: 10.1155/2018/4029371

Abstract

Exponentially fitted and trigonometrically fitted explicit modified Runge-Kutta type (MRKT) methods for solving y x = f x , y , y are derived in this paper. These methods are constructed which exactly integrate initial value problems whose solutions are linear combinations of the set functions e ω x and e - ω x for exponentially fitted and sin ω x and cos ω x for trigonometrically fitted with ω R being the principal frequency of the problem and the frequency will be used to raise the accuracy of the methods. The new four-stage fifth-order exponentially fitted and trigonometrically fitted explicit MRKT methods are called EFMRKT5 and TFMRKT5, respectively, for solving initial value problems whose solutions involve exponential or trigonometric functions. The numerical results indicate that the new exponentially fitted and trigonometrically fitted explicit modified Runge-Kutta type methods are more efficient than existing methods in the literature.

Citation

Download Citation

N. Ghawadri. N. Senu. F. Ismail. Z. B. Ibrahim. "Exponentially Fitted and Trigonometrically Fitted Explicit Modified Runge-Kutta Type Methods for Solving y x = f x , y , y ." J. Appl. Math. 2018 1 - 19, 2018. https://doi.org/10.1155/2018/4029371

Information

Received: 21 December 2017; Revised: 1 May 2018; Accepted: 28 May 2018; Published: 2018
First available in Project Euclid: 19 September 2018

zbMATH: 07000933
MathSciNet: MR3827854
Digital Object Identifier: 10.1155/2018/4029371

Rights: Copyright © 2018 Hindawi

JOURNAL ARTICLE
19 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.2018 • 2018
Back to Top