Title: Basins of attraction and critical curves for Newton-type methods in a phase equilibrium problem
Authors: Gustavo Mendes Platt; Fran Sérgio Lobato; Gustavo Barbosa Libotte; Francisco Duarte Moura Neto
Addresses: Escola de Química e Alimentos, Universidade Federal do Rio Grande, Santo Antônio da Patrulha, RS, Brazil ' Laboratório de Modelagem, Simulação, Controle e Otimização de Processos Químicos, Faculdade de Engenharia Química, Universidade Federal de Uberlândia, Uberlândia, MG, Brazil ' Instituto Politécnico, Universidade do Estado do Rio de Janeiro, Nova Friburgo, RJ, Brazil ' Instituto Politécnico, Universidade do Estado do Rio de Janeiro, Nova Friburgo, RJ, Brazil
Abstract: Many engineering problems are described by systems of nonlinear equations, which may exhibit multiple solutions, in a challenging situation for root-finding algorithms. The existence of several solutions may give rise to complex basins of attraction for the solutions in the algorithms, with severe influence on their convergence behaviour. In this work, we explore the relationship of the basins of attractions with the critical curves (the locus of the singular points of the Jacobian of the system of equations) in a phase equilibrium problem in the plane with two solutions, namely the calculation of a double azeotrope in a binary mixture. The results indicate that the conjoint use of the basins of attraction and critical curves can be a useful tool to select the most suitable algorithm for a specific problem.
Keywords: Newton's methods; basins of attraction; nonlinear systems; phase equilibrium.
International Journal of Computational Science and Engineering, 2020 Vol.23 No.1, pp.91 - 102
Accepted: 17 Mar 2020
Published online: 08 Oct 2020 *