Improving the Accuracy of Chebyshev Tau Method for Nonlinear Differential Problems

• Type: Article in International Scientific Journal
• Date: 2016

Authors

Gavina, A (Author) Other; Matos, J (Author) Other; Vasconcelos, PB (Author) FEP

Journal

Title: Mathematics in Computer Science

Vol. 10 No. 2

Pages: 279-289

ISSN: 1661-8270

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 0 Citations

Other information

Authenticus ID: P-00K-CPB

DOI: 10.1007/s11786-016-0265-1

Abstract (EN): The spectral properties convergence of the Tau method allow to obtain good approximate solutions for linear differential problems advantageously. However, for nonlinear differential problems the method may produce ill-conditioned matrices issued from the approximations obtained in the iterations from the linearization process. In this work we introduce a procedure to approximate nonlinear terms in the differential equations and a new way to build the corresponding algebraic problem improving the stability of the overall algorithm. Introducing the linearization coefficients of orthogonal polynomials in the Tau method within the iterative process, we can go further in the degree to approximate the solution of the differential problems, avoiding the consequences of ill-conditioning. © 2016 Springer International Publishing

Language: English

Type (Professor's evaluation): Scientific