Solving Partial Differential Problems with Tau Toolbox

• Tipo: Artigo em Revista Científica Internacional
• Data: 2024

Autores

Lima, NJ (Autor) Outra; Matos, JMA (Autor) Outra; vasconcelos, pb (Autor) FEP

Revista

Título: Mathematics in Computer Science

Vol. 18

Página Final: 8

ISSN: 1661-8270

Editora: Springer Nature

Indexação

ISI Web of Knowledge - 0 Citações

Scopus - 0 Citações

Outras Informações

ID Authenticus: 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.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 12