Generalized Runge-Kutta Method with respect to the Non-Newtonian Calculus
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...
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Main Authors: | , |
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Format: | Article |
Language: | English |
Published: |
Wiley
2015-01-01
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Series: | Abstract and Applied Analysis |
Online Access: | http://dx.doi.org/10.1155/2015/594685 |
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Summary: | 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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ISSN: | 1085-3375 1687-0409 |