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Solving 2nd order BVPs in planar irregular domains

Author

Listed:
  • Guimarães, O.
  • Labecca, W.
  • Piqueira, José R.C.

Abstract

This paper presents a pseudo-spectral method to solve PDEs in univocally describable irregular planar domains in polar coordinates, using a simple relationship that transforms the problem for the classic case in the unit circle, equipped with an orthogonal bivariate basis and complete in Sobolev sense. Given its generality, it applies to elliptical, parabolic or hyperbolic PDEs in Robin’s condition. The choice of Radau points applied here allows the exclusion of the singularity in the origin and a posteriori error estimate also here developed provides us sharp error bounds of the numerical solution.

Suggested Citation

  • Guimarães, O. & Labecca, W. & Piqueira, José R.C., 2022. "Solving 2nd order BVPs in planar irregular domains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 1-22.
    • Handle: RePEc:eee:matcom:v:201:y:2022:i:c:p:1-22
    DOI: 10.1016/j.matcom.2022.05.005
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    References listed on IDEAS

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    1. Osvaldo Guimarães & José Roberto C. Piqueira & Marcio Lobo Netto, 2010. "Direct Computation of Operational Matrices for Polynomial Bases," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-12, September.
    2. A. H. Bhrawy & D. Baleanu & L. M. Assas & J. A. Tenreiro Machado, 2013. "On a Generalized Laguerre Operational Matrix of Fractional Integration," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-7, March.
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