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Inexact Newton matrix-free methods for solving complex biotechnological systems

In the article a new approach for solving complex and highly nonlinear differential-algebraic equations (DAEs) was presented. An important kind of applications of DAE systems is modeling of biotechnological processes, which can have a very different course. An efficient solving of equations describing biotechnological industrial inlets results in better optimization of the processes and has a positive impact on the environment. Some of the mentioned processes were characterized by a highly nonlinear dynamics. To obtain the trajectories of the state numerically, the backward differentiation formula was used in the presented method. As a result, a large-scale system of nonlinear algebraic equations was obtained. To solve a such system, the inexact Newton matrix-free approach was proposed. The new algorithm was tested on a mathematical model of a fed-batch fermentor for penicillin production. The numerical simulations were executed in MATLAB using Wroclaw Center for Networking and Supercomputing.