Improving the Accuracy of Chebyshev Tau Method for Nonlinear Differential Problems
| Autor: | Alexandra Gavina, Paulo B. Vasconcelos, José Matos |
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| Rok vydání: | 2016 |
| Předmět: |
Iterative and incremental development
Differential equation Applied Mathematics 010102 general mathematics Mathematical analysis 0102 computer and information sciences 01 natural sciences Computational Mathematics Nonlinear system Computational Theory and Mathematics 010201 computation theory & mathematics Linearization Orthogonal polynomials Applied mathematics 0101 mathematics Spectral method Universal differential equation Differential (mathematics) Mathematics |
| Zdroj: | Mathematics in Computer Science. 10:279-289 |
| ISSN: | 1661-8289 1661-8270 |
| DOI: | 10.1007/s11786-016-0265-1 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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