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

Abstract EN

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.