Application of a subdivision algorithm for solving nonlinear algebraic systems - DOI: 10.4025/actascitechnol.v30i1.3198

• Autor(a) principal: Corazza, Fernanda de Castilhos
• Data de Publicação: 2008
• Outros Autores: Oliveira, José Vladimir de, Corazza, Marcos Lúcio
• Tipo de documento: Artigo
• Idioma: por; eng
• Título da fonte: Acta scientiarum. Technology (Online)
• Texto Completo: http://www.periodicos.uem.br/ojs/index.php/ActaSciTechnol/article/view/3198
• topic: numerical analysis; nonlinear equations; multiple solutions; subdivision algorithm; simulation; chemical engineering processes; análise numérica; equações não lineares; múltiplas soluções; algoritmo de subdivisão; simulação; processos de engenharia química; 3.06.00.00-6 Engenharia Química

A subdivision algorithm is presented and applied to solving commonly found chemical engineering problems described by nonlinear algebraic systems. For this purpose, a web-based library available in the literature was used as the main source to select a wide class of one- and multidimensional problems, comprising phase and chemical equilibrium, conversion in tubular and continuous stirred tank reactors, material and energy balances, etc. The problems are classified according to the literature as low, intermediate and of high degree of numerical difficulty based on specific characteristics, like discontinuities in the functions, multiple solutions with the occurrence of false and unfeasible roots, and the presence of null derivative values. It is shown that the algorithm is efficient and robust, even for multidimensional problems of high numerical difficulty, allowing to find simultaneously all the feasible roots of nonlinear algebraic systems, naturally excluding false and unfeasible solutions, with a relatively low CPU time. These features make the algorithm an interesting alternative to deal with chemical engineering problems in contrast to some methods currently in the literature.