Approximating the solution of integro-differential problems via the spectral Tau method with filtering

• Tipo: Artigo em Revista Científica Internacional
• Data: 2020

Autores

Matos, JC (Autor) Outra; Maria Joao Rodrigues (Autor) FCUP; Rodrigues, MJ (Autor) Outra; vasconcelos, pb (Autor) FEP

Revista

Título: Applied Numerical Mathematics

Vol. 149 Nº SI

Páginas: 164-175

ISSN: 0168-9274

Editora: Elsevier

Indexação

ISI Web of Knowledge - 2 Citações

Scopus - 1 Citação

Outras Informações

ID Authenticus: P-00Q-NVD

DOI: 10.1016/j.apnum.2019.05.025

Abstract (EN): Computing approximate solutions of integro-differential problems can be difficult and time consuming, requiring large expertize. Tau Toolbox is a numerical library that produces approximate polynomial solutions of differential, integral and integro-differential equations via the spectral Lanczos' Tau method. This approach, however, may fail to ensure the spectral rate of convergence, and even to reach convergence, whenever the exact solution shows singularities. This paper describes a post-processing phase based on a Frobenius-Padé approximation method to build rational approximations from the polynomial Tau approximation. This filtering extension improves the accuracy of the spectral approximation when working in the vicinity of solutions with singularities. Furthermore, some insights on how to perform such a filtering process on a piecewise version of the Tau method to tackle larger domains and/or stiff problems are offered. © 2019 IMACS

Idioma: Inglês

Tipo (Avaliação Docente): Científica