In this article we explore a series of advanced mathematical methods aimed at solving nonlinear equations, including globalization strategies, sensitivity analysis, and automatic differentiation. Additionally, special capabilities such as automatic exploitation of sparsity and the use of Krylov methods for solving nonlinear systems are described.
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The document also examines the robustness of these methods applied to various test problems, including the Doyle-Fuller-Newman battery model and large-scale nonlinear systems. These approaches are fundamental to improving accuracy and efficiency in applied mathematical modeling.
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