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2015 Generalized Runge-Kutta Method with respect to the Non-Newtonian Calculus
Uğur Kadak, Muharrem Özlük
Abstr. Appl. Anal. 2015: 1-10 (2015). DOI: 10.1155/2015/594685


Theory and applications of non-Newtonian calculus have been evolving rapidly over the recent years. As numerical methods have a wide range of applications in science and engineering, the idea of the design of such numerical methods based on non-Newtonian calculus is self-evident. In this paper, the well-known Runge-Kutta method for ordinary differential equations is developed in the frameworks of non-Newtonian calculus given in generalized form and then tested for different generating functions. The efficiency of the proposed non-Newtonian Euler and Runge-Kutta methods is exposed by examples, and the results are compared with the exact solutions.


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Uğur Kadak. Muharrem Özlük. "Generalized Runge-Kutta Method with respect to the Non-Newtonian Calculus." Abstr. Appl. Anal. 2015 1 - 10, 2015.


Published: 2015
First available in Project Euclid: 15 April 2015

zbMATH: 1347.65122
MathSciNet: MR3312748
Digital Object Identifier: 10.1155/2015/594685

Rights: Copyright © 2015 Hindawi

Vol.2015 • 2015
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