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

Author

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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.

Suggested Citation

  • Uğur Kadak & Muharrem Özlük, 2015. "Generalized Runge‐Kutta Method with respect to the Non‐Newtonian Calculus," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnlaaa:v:2015:y:2015:i:1:n:594685
    DOI: 10.1155/2015/594685
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    References listed on IDEAS

    as
    1. Ahmet Faruk Çakmak & Feyzi Başar, 2014. "Certain Spaces of Functions over the Field of Non‐Newtonian Complex Numbers," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Uğur Kadak & Hakan Efe, 2014. "The Construction of Hilbert Spaces over the Non-Newtonian Field," International Journal of Analysis, Hindawi, vol. 2014, pages 1-10, October.
    3. Ahmet Faruk Çakmak & Feyzi Başar, 2014. "Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-12, April.
    4. Sebiha Tekin & Feyzi Başar, 2013. "Certain Sequence Spaces over the Non‐Newtonian Complex Field," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Sebiha Tekin & Feyzi Başar, 2013. "Certain Sequence Spaces over the Non-Newtonian Complex Field," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, June.
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