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Improving the Accuracy of Chebyshev Tau Method for Nonlinear Differential Problems

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Abstract

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.

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Authors and Affiliations

  1. Laboratório Engenharia Matemática, Instituto Superior Engenharia Porto, Porto, Portugal

    Alexandra Gavina & José Matos

  2. Center of Mathematics at the University of Porto, Porto, Portugal

    José Matos & Paulo Vasconcelos

  3. Faculty of Economics of the University of Porto, Porto, Portugal

    Paulo Vasconcelos

Authors
  1. Alexandra Gavina
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  2. José Matos
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  3. Paulo Vasconcelos
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Corresponding author

Correspondence to Alexandra Gavina.

Additional information

J. Matos and P. Vasconcelos were partially supported by CMUP (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European structural funds (FEDER), under the partnership agreement PT2020.

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Gavina, A., Matos, J. & Vasconcelos, P. Improving the Accuracy of Chebyshev Tau Method for Nonlinear Differential Problems. Math.Comput.Sci. 10, 279–289 (2016). https://doi.org/10.1007/s11786-016-0265-1

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  • DOI: https://doi.org/10.1007/s11786-016-0265-1

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