Scaled Runge-Kutta algorithms are presented for orders 4 and 5, along with accuracy comparisons between the defining algorithms and their scaled versions for a test problem.

Abstract A system of ordinary differential equations (ODEs) is produced by the semi-discretize method of discretizing the advection diffusion equation (ADE). Runge-Kutta methods of the second and ...

In this paper the order conditions for Runge-Kutta methods are presented based on Butcher's rooted tree theory. A new Runge-Kutta method of order four (MINRK4) ...

In order to maintain the same order of convergence, the classical fourth-order Runge-Kutta method is the preferred method for explicit time integration. Soliton-type solutions are used to evaluate the ...