Numerical sorting-based optimization as applied to general differential and nonlinear equations

Abstract

Parallelized algorithms for the localization and computation of the extrema of functions applied to find approximate solutions of systems of nonlinear equations are outlined. It is shown that they can be used to find the extrema of difference solutions of systems of ordinary differential equations and to perform an analysis for Lyapunov stability. The algorithms are based on sorting a sequence with biunique correspondence of input and output indices, extrema being localized by comparing indices without error accumulation.Keywords: numerical optimization, parallel localization of extrema, approximate solution of systems of nonlinear equations, sorting, stability under perturbation of parameters.