Numerical study of third-order ordinary differential equations using a new class of two derivative Runge-Kutta type methods

Citation

Lee, Khai Chien and Senu, Norazak and Ahmadian, Ali and Ibrahim, Siti Nur Iqmal and Baleanu, D. (2020) Numerical study of third-order ordinary differential equations using a new class of two derivative Runge-Kutta type methods. Alexandria Engineering Journal, 59 (4). 2449 - 2467. ISSN 1110-0168; ESSN: 2090-2670

Abstract

This study introduces new special two-derivative Runge-Kutta type (STDRKT) methods involving the fourth derivative of the solution for solving third-order ordinary differential equations. In this regards, rooted tree theory and the corresponding B-series theory is proposed to derive order conditions for STDRKT methods. Besides, explicit two-stages fifth order and three-stages sixth order STDRKT methods are derived and stability,consistency and convergence of STDRKT methods are analysed in details. Accuracy and effectiveness of the proposed techniques are validated by a number of various test problems and compared to existing methods in the literature.

Download File

Text
Numerical study of third-order ordinary differential equations.pdf
Download (6kB)

Official URL or Download Paper: https://www.sciencedirect.com/journal/alexandria-e...

Additional Metadata

Item Type:	Article
Divisions:	Faculty of Science Institute for Mathematical Research
DOI Number:	https://doi.org/10.1016/j.aej.2020.03.008
Publisher:	Elsevier
Keywords:	Runge-Kutta type methods; B-series; Rooted tree; Third-order ordinary differential equations; Algebraic order
Depositing User:	Mohamad Jefri Mohamed Fauzi
Date Deposited:	10 Jan 2022 04:13
Last Modified:	10 Jan 2022 04:13
Altmetrics:	http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1016/j.aej.2020.03.008
URI:	http://psasir.upm.edu.my/id/eprint/86938
Statistic Details:	View Download Statistic

Actions (login required)

View Item