Browsing by Author "Adnan, Zakaria"

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    An analysis of Runge-Kutta method in non-Newtonian calculus
    (JUNE, 2015 ) Adnan, Zakaria
    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.