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Trigonometrically-fitted higher order two derivative Runge-Kutta method for solving orbital and related periodical IVPs

N. A. Ahmad [1] , N. Senu [2] , F. Ismail [3]

In this paper, a trigonometrically-fitted two derivative Runge-Kutta method (TFTDRK) of high algebraic order for the numerical integration of first order Initial Value Problems (IVPs) which possesses oscillatory solutions is constructed. Using the trigonometrically-fitted property, a sixth order four stage Two Derivative Runge-Kutta (TDRK) method is designed. The numerical experiments are carried out with the comparison with other existing Runge-Kutta methods (RK) to show the accuracy and efficiency of the derived methods.
two derivative Runge-Kutta method, trigonometrically-fitted, ordinary differential equations, initial value problems
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Birincil Dil en Matematik Matematik Orcid: 0000-0003-3007-0432Yazar: N. A. Ahmad (Sorumlu Yazar) Orcid: 0000-0001-8614-8281Yazar: N. Senu Orcid: 0000-0002-1548-8702Yazar: F. Ismail Yayımlanma Tarihi : 8 Ekim 2019
 Bibtex @araştırma makalesi { hujms629826, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2019}, volume = {48}, pages = {1312 - 1323}, doi = {}, title = {Trigonometrically-fitted higher order two derivative Runge-Kutta method for solving orbital and related periodical IVPs}, key = {cite}, author = {Ahmad, N. A. and Senu, N. and Ismail, F.} } APA Ahmad, N , Senu, N , Ismail, F . (2019). Trigonometrically-fitted higher order two derivative Runge-Kutta method for solving orbital and related periodical IVPs. Hacettepe Journal of Mathematics and Statistics , 48 (5) , 1312-1323 . Retrieved from https://dergipark.org.tr/tr/pub/hujms/issue/49321/629826 MLA Ahmad, N , Senu, N , Ismail, F . "Trigonometrically-fitted higher order two derivative Runge-Kutta method for solving orbital and related periodical IVPs". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1312-1323 Chicago Ahmad, N , Senu, N , Ismail, F . "Trigonometrically-fitted higher order two derivative Runge-Kutta method for solving orbital and related periodical IVPs". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1312-1323 RIS TY - JOUR T1 - Trigonometrically-fitted higher order two derivative Runge-Kutta method for solving orbital and related periodical IVPs AU - N. A. Ahmad , N. Senu , F. Ismail Y1 - 2019 PY - 2019 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1312 EP - 1323 VL - 48 IS - 5 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2018 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Trigonometrically-fitted higher order two derivative Runge-Kutta method for solving orbital and related periodical IVPs %A N. A. Ahmad , N. Senu , F. Ismail %T Trigonometrically-fitted higher order two derivative Runge-Kutta method for solving orbital and related periodical IVPs %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 5 %R %U ISNAD Ahmad, N. A. , Senu, N. , Ismail, F. . "Trigonometrically-fitted higher order two derivative Runge-Kutta method for solving orbital and related periodical IVPs". Hacettepe Journal of Mathematics and Statistics 48 / 5 (Ekim 2019): 1312-1323 . AMA Ahmad N , Senu N , Ismail F . Trigonometrically-fitted higher order two derivative Runge-Kutta method for solving orbital and related periodical IVPs. Hacettepe Journal of Mathematics and Statistics. 2019; 48(5): 1312-1323. Vancouver Ahmad N , Senu N , Ismail F . Trigonometrically-fitted higher order two derivative Runge-Kutta method for solving orbital and related periodical IVPs. Hacettepe Journal of Mathematics and Statistics. 2019; 48(5): 1323-1312.