التفاصيل البيبلوغرافية
| العنوان: |
A Sparse Differential Algebraic Equation (DAE) and Stiff Ordinary Differential Equation (ODE) Solver in Maple |
| المؤلفون: |
Jang, Taejin, Uppaluri, Maitri, Seo, Kyeongjun, Ramadesigan, Venkatasailanathan, Subramanian, Venkat |
| المصدر: |
Maple Transactions; Vol. 3 No. 4 (2023): Winter Issue ; 2564-3029 |
| بيانات النشر: |
Western Libraries, University of Western Ontario |
| سنة النشر: |
2024 |
| مصطلحات موضوعية: |
sparse solver, analytical jacobian, index-1 dae |
| الوصف: |
This paper implements efficient numerical methods in Maple to solve index-1 nonlinear Differential Algebraic Equations (DAEs) and stiff Ordinary Differential Equations (ODEs) systems. Single-step methods (like Trapezoid (TR), Implicit-mid point (IMP), Euler-backward (EB), Radau IIA (Rad) methods, TRBDF2, TRX2) and backward-difference formula of order 2 are implemented with adaptive time-stepping methods in Maple to solve index-1 nonlinear DAEs. Maple’s robust and efficient ability to search within a list/set is exploited to identify the sparsity pattern and automatically calculate the analytic Jacobian. The algorithm and implementation are robust and efficient for index-1 DAE problems and scale well for finite difference/finite element discretization of two-dimensional models with system size up to 10,000 nonlinear DAEs and solve the same in a few seconds. The computational efficiency of the proposed algorithm (provided as an open-access code) compares favorably with the commercial solver gPROMs, one of the most commonly used sparse DAE solvers in the industry. |
| نوع الوثيقة: |
article in journal/newspaper |
| وصف الملف: |
application/pdf |
| اللغة: |
English |
| Relation: |
https://mapletransactions.org/index.php/maple/article/view/16701/13115; https://mapletransactions.org/index.php/maple/article/view/16701 |
| الاتاحة: |
https://mapletransactions.org/index.php/maple/article/view/16701 |
| Rights: |
Copyright (c) 2024 Taejin Jang, Maitri Uppaluri, Kyeongjun Seo, Venkatasailanathan Ramadesigan, Venkat Subramanian ; https://creativecommons.org/licenses/by/4.0/deed.en |
| رقم الانضمام: |
edsbas.144E6BF1 |
| قاعدة البيانات: |
BASE |