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

• Type: Article in International Scientific Journal
• Date: 2020

Authors

Matos, JC (Author) Other; Maria Joao Rodrigues (Author) FCUP; Rodrigues, MJ (Author) Other; vasconcelos, pb (Author) FEP

Journal

Title: Applied Numerical Mathematics

Vol. 149 No. SI

Pages: 164-175

ISSN: 0168-9274

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 2 Citations

Scopus - 1 Citation

Other information

Authenticus ID: 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

Language: English

Type (Professor's evaluation): Scientific