An analysis of Runge-Kutta method in non-Newtonian calculus

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JUNE, 2015
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Non-Newtonian Calculus or Multiplicative calculus can be used as a tool wherever a problem is of exponential (relational) in nature. In this thesis the derivation of the Runge-Kutta Method in the framework of non-Newtonian (Multiplicative) Calculus is presented. The non-Newtonian (Multiplicative) Runge-Kutta Methods of orders 2, 3, and 4 are developed and discussed. The non-Newtonian (Multiplicative) Runge-Kutta Method is tested on some selected examples where the solutions of the ordinary differential equations are known using developed Matlab codes. The results show that for certain family of initial value problem the non-Newtonian (Multiplicative) Runge-Kutta method gives better results to the Ordinary Runge-Kutta method.
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfillment of the requirement for the Degree of Master of Science in Industrial Mathematics.