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

作者：Motsa Sandile S^*

来源：Central European Journal of Physics, 2012, 10(4): 936-946.

DOI：10.2478/s11534-011-0124-2

• successive linearization method
• Lotka-Voltera
• Rossler attactor
• Genisio-Tesi system
• Lorenz system
• chaotic system

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, Rossler 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.

• 出版日期2012-8