Accurate Multistep Multi-derivative Collocation Methods Applied to Chaotic Systems

Abstract

Accurate multistep multi-derivative collocation methods are derived for the numerical integration of chaotic systems. These methods have high order of accuracy, with A-stable regions of absolute stability. Although the calculation of the third derivative terms in the methods is relatively high compared to the rst and second derivative terms, the advantage gained makes them suitable for solving chaotic system of equations with large eigenvalues. The stability characteristic properties and order of accuracy of the methods are studied. Figurative comparisons of the solution curves obtained are in good agreement with the exact solutions which demonstrate practically the eectiveness of the proposed methods.