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

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  • Uğur Kadak
  • Muharrem Özlük

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.

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Handle: RePEc:wly:jnlaaa:v:2015:y:2015:i:1:n:594685
DOI: 10.1155/2015/594685
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