A new piecewise-quasilinearization method for solving chaotic systems of initial value problems

Sandile Motsa 1
  • 1 School of Mathematical Sciences, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg, 3209, South Africa

Abstract

In this paper, a modification of the successive linearization method (SLM) for solving nonlinear initial value problems is introduced for the first time. The proposed method is based on a novel technique of extending the standard SLM and adapting it to a sequence of multiple intervals. In this new application the method is referred to as the piecewise successive linearization method(PSLM). This new algorithm is applied to chaotic and non-chaotic differential equations that model the Lotka-Volterra, Lorenz, Rössler and Genesio-Tesi systems. A comparative study between the new algorithm and the MATLAB Runge-Kutta based in-built solver (ode45) method is presented. The results demonstrate accuracy and reliability of the proposed PSLM algorithm.

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