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Improving the Accuracy of Chebyshev Tau Method for Nonlinear Differential Problems

Title
Improving the Accuracy of Chebyshev Tau Method for Nonlinear Differential Problems
Type
Article in International Scientific Journal
Year
2016
Authors
Gavina, A
(Author)
Other
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Matos, J
(Author)
Other
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Vasconcelos, PB
(Author)
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Journal
Vol. 10 No. 2
Pages: 279-289
ISSN: 1661-8270
Publisher: Springer Nature
Indexing
Other information
Authenticus ID: P-00K-CPB
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
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