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Fourth-order improved Runge–Kutta method for directly solving special third-order ordinary differential equations


Citation

Hussain, Kasim Abbas and Ismail, Fudziah and Senu, Norazak and Rabiei, Faranak (2017) Fourth-order improved Runge–Kutta method for directly solving special third-order ordinary differential equations. Iranian Journal of Science and Technology, Transactions A: Science, 41 (2). pp. 429-437. ISSN 1028-6276; ESSN: 2364-1819

Abstract

In this paper, fourth-order improved Runge–Kutta method (IRKD) for directly solving a special third-order ordinary differential equation is constructed. The fourth-order IRKD method has a lower number of function evaluations compared with the fourth-order Runge–Kutta method. The stability polynomial of the method is given. Numerical comparisons are also performed using the existing Runge–Kutta method after reducing the problems into a system of first-order equations and solving them, and direct RKD method for solving special third-order ordinary differential equations. Numerical examples are presented to illustrate the efficiency and the accuracy of the new method in terms of number of function evaluations as well as max absolute error.


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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
DOI Number: https://doi.org/10.1007/s40995-017-0258-1
Publisher: Springer
Keywords: Special third-order; Ordinary differential equations; Runge–Kutta method; IRKD method
Depositing User: Nabilah Mustapa
Date Deposited: 08 Sep 2017 10:29
Last Modified: 08 Sep 2017 10:29
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1007/s40995-017-0258-1
URI: http://psasir.upm.edu.my/id/eprint/57202
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