A practical solution to the numerical butterfly effect in chaotic systems for fast but memory limited computers

Abstract

The sensitive dependence on initial conditions found in nonlinear chaotic systems is known as the “butterfly effect”. Such systems when numerically analyzed can exhibit a convergence instability when employing standard numerical methods. Presented here is a practical numerical method for eliminating the “under-resolution” problem observed when solving for solutions to nonlinear chaotic systems with fast but memory limited computers. The proposed idea of using a micro-integrator loop was applied with the Modified Euler Method of numerical integration. The improvement offered by combining the micro-integrator loop with the classical integration scheme created an avenue for achieving convergence using much less memory than would be required if the micro-integrator loop was not employed.