Solución Numérica de una Ecuación Diferencial usando el Método de Galerkin y Wavelets B-Splines Cardinales

Authors

  • Ronald León Navarro

DOI:

https://doi.org/10.17268/sel.mat.2014.01.01

Keywords:

Metodo Galerkin, bases, wavelets, B-splines, Analisis Multiresolución, ED elíptica

Abstract

En el presente artculo, resolvemos numericamente una ecuacion diferencial ordinaria elptica con condiciones de frontera tipo Dirichlet. El tratamiento numerico se realiza usando el clasico metodo de Galerkin y un tipo especial de bases wavelets; estas son wavelets B-splines cardinales. Los resultados de la experimentacion numerica realizada muestran que, aun considerando coecientes, y
funcion en el segundo miembro, de la ecuacion diferencial, como funciones discontinuas con salto nito grande, el sistema que se genera es estable si se aplica precondicionamiento y la solucion numerica es sucientemente exacta para bajos niveles de aproximacion.

References

K. Amaratunga, J. Williams, S. Qian y J. Weiss, Wavelet-Galerkin solutions for one dimensional partial dierential equations, IESL Technical Report No. 92-05, Intelligent Engineering Systems Laboratory, M.I.T., 1992.

G. Beylkin, R. Coifman y V. Rokhlin, Fast wavelet transforms and numerical algorithms I, Comm. Pure Appl. Math., 44(1991) pp. 141-183.

H. Brezis, Analisis Funcional, Alianza Editorial S.A., Madrid, 1984.

R. Burgos, R. Silva y M. Santos, Direct solution of dierential equations using the wavelet-Galerkin method, Mecanica Computacional, 29(2010) pp. 4573-4584.

C. Chui y J-Z Wang, On Compactly Spline Wavelets and a Duality Principle, Transactions of the American Mathematical Society, 330 (1992) pp. 903-915.

I. Daubechies, Ten Lectures on Wavelets, SIAM Publications, Philadelphia, 1992.

W. R. Glowinski, W. Lawton, M. Ravachol y E. Tenenbaum, Wavelet solution of linear and nonlinear elliptic, parabolic and hyperbolic problems in one space dimension, Proc. 9th International Conference on Numerical Methods in Applied Sciences and Engineering, SIAM, Philadelphia, 1990.

S. Kesavan, Topics in Functional Analysis and Applications, Wiley Eastern Limited, New Delhi, 1989.

W. Lawton, W. Morrell, E. Tenebaum, y J. Weiss, The wavelet galerkin method for partial dierential equations, Technical Report AD901220, Aware, Inc., 1990.

A. Louis, D. Maass y A. Rieder, Wavelets: Theory and Applications, Johb-Wiley & Sons, USA, 1997.

S. Mallat, A wavelet tour of signal processing, Academic Press, San Diego, 1999.

M. Nair, Wavelet-Galerkin Method, Talk at QIP-short Term Course, Department of Mathematics, IIT Madras, Diciembre, 2004.

H. Nguyen y G. Evangelista, A continuous wavelet-Galerkin method for the linear wave equation [Elektronisk resurs], SIAM Journal on Scientic Computing., 2007

http://liu.diva-portal.org/smash/get/diva2:24195/FULLTEXT01

S. Qian y J. Weiss, Wavelets and the numerical solution of partial dierential equations, Journal of Computational Physics, 106 (1992) pp. 155-175.

K. Urban, Wavelets in Numerical Simulation Problem Adapted Construction and Applications, Ed. Springer, Heilderberg, 2002.

K. Urban, Wavelet Methods for Elliptic Partial Dierential Equations, Oxford Science Publications, Oxford, 2009.

J. Wang, Cubic spline wavelet Bases of Sobolev spaces and multilevel interpolation, Appl. Compu. Harm. Anal., 3 no.2 (1996) pp. 154-163.

R. Wells y X. Zhou, Wavelet Solutions for the Dirichlet Problem, AFOSR Technical Report No. 90-0334, Aware, Inc., 1993.

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Published

2014-04-05

How to Cite

Navarro, R. L. (2014). Solución Numérica de una Ecuación Diferencial usando el Método de Galerkin y Wavelets B-Splines Cardinales. Selecciones Matemáticas, 1(01). https://doi.org/10.17268/sel.mat.2014.01.01

Issue

Vol. 1 No. 01 (2014): January - July

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Articles

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