A Sparse DAE Solver in Maple

12/05/2022

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by   Taejin Jang, et al.

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In this paper, some adaptive single-step methods like Trapezoid (TR), Implicit-mid point (IMP), Euler-backward (EB), and Radau IIA (Rad) methods are implemented in Maple to solve index-1 nonlinear Differential Algebraic Equations (DAEs). Maple's robust and efficient ability to search within a list/set is exploited to identify the sparsity pattern and the analytic Jacobian. The algorithm and implementation were found to be robust and efficient for index-1 DAE problems and scales well for finite difference/finite element discretization of two-dimensional models with system size up to 10,000 nonlinear DAEs and solves the same in few seconds.