Generalized Runge-Kutta Method with respect to the Non-Newtonian Calculus
Open Access
- 5 February 2015
- journal article
- research article
- Published by Hindawi Limited in Abstract and Applied Analysis
- 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.Keywords
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