Resolução de um Problema Inverso Diferencial Fracionário no Processo de Fermentação Batelada Usando o Método da Colocação Ortogonal e o Algoritmo de Busca Fractal Estocástica

F. S. Lobato

Abstract


A presente contribuição tem como objetivo desenvolver uma ferramenta numérica para a resolução de problemas inversos modelados por equações diferenciais ordinárias com ordem fracionária. Esta consiste da associação entre o Método da Colocação Ortogonal no contexto fracionário com o algoritmo de Busca Fractal Estocástica. Os resultados obtidos com a extensão do Método da Colocação Ortogonal em funções matemáticas demonstraram a habilidade desta estratégia em comparação com outras abordagens numéricas. Para fins de ilustração, um problema inverso que consiste na determinação dos parâmetros de um modelo e da ordem fracionária do processo de fermentação da enzima lacase é proposto e resolvido. Em relação a este estudo pode-se concluir que o aumento do número de graus de liberdade (ordem fracionária é mais uma variável de projeto) aumenta a chance de um melhor ajuste do modelo aos pontos experimentais.


Keywords


Problemas Inversos; Equações Diferenciais Ordinárias Fracionárias; Busca Fractal Estocástica; Fermentação Batelada

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DOI: https://doi.org/10.5540/tema.2020.021.03.537

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