A Sparse DAE Solver in Maple

TL;DR

This paper presents an implementation of adaptive single-step methods for solving large-scale index-1 nonlinear DAEs in Maple, demonstrating robustness and efficiency for problems with up to 10,000 equations.

Contribution

It introduces a novel approach leveraging Maple's capabilities to efficiently identify sparsity and Jacobians, enabling scalable DAE solutions.

Findings

Efficiently solves large-scale DAEs with up to 10,000 equations.

Robust implementation of multiple adaptive single-step methods.

Scales well for finite difference and finite element discretizations.

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.