A Sparse DAE Solver in Maple
Numerical Analysis
2022-12-23 v2 Numerical Analysis
Abstract
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.
Cite
@article{arxiv.2212.02630,
title = {A Sparse DAE Solver in Maple},
author = {Taejin Jang and Maitri Uppaluri and Venkat R. Subramanian},
journal= {arXiv preprint arXiv:2212.02630},
year = {2022}
}