Higher-order Runge-Kutta algorithms

Abstract

Rung-Kutta algorithms played an important role for solving some types of the partial differential equations that are hard to get their solution analytically. It was found that there is an infinite number of Rung-Kutta algorithms starting from stage two according to the values of the parameters. It is not possible to decide which of these algorithms of the same stage is better than others when solving a certain problem, because it depends on the differential equation itself, the step chosen also affects the solution. In this work, we drive Rung-Kutta algorithms of high stages, which is Rung-Kutta algorithms from stage five to seven.