An analysis of Runge-Kutta method in non-Newtonian calculus
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Date
JUNE, 2015
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Abstract
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.
Description
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.