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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 5

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

N. A. Ahmad
N. Senu
F. Ismail
Sayfa
1312–1323
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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.
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Temel Bulgular & Veri:Using the trigonometrically-fitted property, a sixth order four stage Two Derivative Runge-Kutta (TDRK) method is designed.
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Sonuç & Katkı: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.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:two derivative Runge-Kutta method · trigonometrically-fitted · ordinary differential equations

Abstract

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.

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Bu Makaleye Atıf Yap

Ahmad, N. A., Senu, N., Ismail, F. (2022). Trigonometrically-fitted higher order two derivative Runge-Kutta method for solving orbital and related periodical IVPs. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 5, 1312–1323. https://ajindex.com/articles/530142

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Kaynakça (13)

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  7. M.A. Demba, N. Senu and F. Ismail, Trigonometrically-fitted explicit four-stage fourth-order Runge-Kutta-Nyström method for the solution of initial value problems with oscillatory behavior, Global Journal of Pure and Applied Mathematics, 12 (1), 67-80, 2016
  8. M.A. Demba, N. Senu and F. Ismail, Fifth-Order Four-Stage Explicit Trigonometrically-Fitted Runge-Kutta-Nyström Methods, Recent Advances in Math- ematical Sciences, 27-36, 2016
  9. M.A. Demba, N. Senu and F. Ismail, A 5(4) Embedded Pair of Explicit Trigonometrically-Fitted Runge-Kutta-Nyström Methods for the Numerical Solution of Oscillatory Initial Value Problems, Math. Comput. Appl. 21 (4), 46, 2016
  10. M.A. Demba, N. Senu and F. Ismail, A symplectic explicit trigonometrically-fitted Runge-Kutta-Nyströ method for the numerical solution of periodic problems, Int. J. Appl. Eng. Res. 11 (11), 7495-7500, 2016
  11. M.A. Demba, N. Senu and F. Ismail, An Embedded 4(3) Pair of Explicit Trigonometrically-Fitted Runge-Kutta-Nyström Method for Solving Periodic Initial Value Problems, Appl. Math. Sci. 17, 819-838, 2017
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