Bivariate Legendre approximation
DOI:
https://doi.org/10.14419/ijamr.v6i4.8198Keywords:
Two-dimensional Legendre basis, Three terms recurrence construction, Error Estimation.Abstract
Spectral methods are among the numerical methods commonly used for approximating solutions of boundary value problems. In this paper we propose, a generalization of the spectral Tau method in dimension 2, this method is generalized by the use of a new two-dimensional polynomial basis constructed by a three terms recurrence relation. We also present an estimation of error committed by the proposed method.
References
[1] A.Quarteroni, A. Valli, Numerical Approximations of Partial Differential Equations, (Springer, Heidelberg) 1994.
[2] A.Quarteroni, C. Canuto, M. Y. Hussaini, T. A. Zang, Spectral Methods Fundamentals in Single Domains, Springer 2006, ISBN : 987-3-540-30725-9 http ://www.dimat.polito.it/chqz/software.
[3] A.Costa, Spectral Methods for Partial Differential Equations, A Mathematical Journal Vol. 6, No; 4, (1-32), december 2004.
[4] B.Costa, L. Dettori, D. Gottlieb and R. Temam, Time Marching Techniques for the Nonlinear Galerkin Method, SIAM Journal of Sci. Comput., Vol. 23 (2001),No. 1, pp. 46-65.
[5] B.Canuto, M. Yousuff Hussaini, Alfio Quarteroni, & Thomas A. Zang, Spectral Methods in Fluid Dynamics. Springer Series in Computational Physics. Springer, 1987.
[6] J. Boyd, Chebyshev and Fourier Spectral Methods, Second Edition, University of Michigan. 2000. Available online: http://www-personal.umich.edu/~jpboyd/BOOK Spectral2000.html.
[7] M.Druon, Mod`elisation du mouvement par polynomes orthogonaux : application 'a l''etude d''coulements fluides. PhD thesis, Universit`e de Poitiers, 2009.
[8] S.Orszag,Numerical analysis of spectral methods, Society for Industrial and Applied Mathematics, Philadelphia 1977.
[9] S.A.Orszag,Spectral methods for problems in complex geometries J. Comput. Phys. 37, 70-92, 1980
[10]Iserles.A First Course in the Numerical Analysis of Differential Equations 2009
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Received date: August 6, 2017
Accepted date: September 20, 2017
Published date: October 27, 2017