Generalized Runge-Kutta Method with respect to the Non-Newtonian Calculus

Uğur Kadak and Muharrem Özlük

Abstract and Applied Analysis, 2015, vol. 2015, 1-10

Abstract:

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.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:594685

DOI: 10.1155/2015/594685

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