Solving Partial Differential Problems with Tau Toolbox

• Type: Article in International Scientific Journal
• Date: 2024

Authors

Lima, NJ (Author) Other; Matos, JMA (Author) Other; vasconcelos, pb (Author) FEP

Journal

Title: Mathematics in Computer Science

Vol. 18

Final page: 8

ISSN: 1661-8270

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 0 Citations

Other information

Authenticus ID: P-010-E7C

DOI: 10.1007/s11786-024-00580-3

Abstract (EN): This paper briefly examines how literature addresses the numerical solution of partial differential equations by the spectral Tau method. It discusses the implementation of such a numerical solution for PDE's presenting the construction of the problem's algebraic representation and exploring solution mechanisms with different orthogonal polynomial bases. It highlights contexts of opportunity and the advantages of exploring low-rank approximations and well-conditioned linear systems, despite the fact that spectral methods usually give rise to dense and ill-conditioned matrices. It presents Tau Toolbox, a Python numerical library for the solution of integro-differential problems. It shows numerical experiments illustrating the implementations' accuracy and computational costs. Finally, it shows how simple and easy it is to use the Tau Toolbox to obtain approximate solutions to partial differential problems.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 12