Runge-Heun-Kutta Methods for Nonlinear Fractional Order Differential Equations

6 Pages Posted: 9 Nov 2018

Date Written: July 2018

Abstract

In this paper, we develop Runge-Heun-Kutta methods for the numerical solution for fractional order differential equations (FDE), whereby both explicit and implicit methods are developed. Based on Heun’s insight of interpreting Runge’s method as a generalization of Gaussian quadrature, we develop methods that are backwards compatible with classic Runge-Kutta methods such as Heun’s method with third order truncation error. Finally, we devise a new approach for treating any nonlinear FDE with multiple fractional order derivatives of any arbitrary order. The methods are tested with some of the more difficult benchmark problems for nonlinear FDE.

Suggested Citation

Harker, Matthew, Runge-Heun-Kutta Methods for Nonlinear Fractional Order Differential Equations (July 2018). Proceedings of International Conference on Fractional Differentiation and its Applications (ICFDA) 2018. Available at SSRN: https://ssrn.com/abstract=3281668 or http://dx.doi.org/10.2139/ssrn.3281668

Matthew Harker (Contact Author)

University of Leoben ( email )

Leoben, A-8700
Austria

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