Multiplicative Runge-Kutta Methods

ABSTRACT: In this thesis the multiplicative Runge-Kutta Method is developed employing the idea of the ordinary Runge-Kutta Method to multiplicative calculus. The multiplicative Runge-Kutta Methods for the orders 2,3, and 4 are developed and discussed. The developed algorithms are applied to examples where the solutions of the Ordinary Differential Equations are known. This gives the opportunity to check the relative error of the calculation reliably. The results in the multiplicative case are also compared with the results from the ordinary Runge-Kutta Methods of the corresponding order. We can see that the Multiplicative Runge-Kutta Method is advantageous to the ordinary Runge-Kutta method of the same order if the solution is of exponential nature. Finally for completeness the multiplicative Finite Difference method is also presented. Keywords: Multiplicative Calculus, Runge-Kutta-Method, Ordinary Differential Equations,Numerical Solution. ……………………………………………………………………………………………………………………………………………………………………………………………………………………