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

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.

Abstract licence: CC BY-NC-ND

30 more references, whose wording the paper’s licence keeps private.

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.