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Journals / 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
Pages
1312–1323
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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 Key Takeaways

🎯
Objective & Hypothesis: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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Key Findings & Data:Using the trigonometrically-fitted property, a sixth order four stage Two Derivative Runge-Kutta (TDRK) method is designed.
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables: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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Cite This Article

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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References (13)

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