On some applications of the wavelet Galerkin method for boundary value problems
Matematičeskoe modelirovanie, Tome 15 (2003) no. 5, pp. 61-70.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we construct a MRA on $(0,1)$ based on the GP functions introduced previously. Then we use such a Multiresolution on the interval to numerically solve a boundary differential problem. The results display the efficiency of the proposed method.
@article{MM_2003_15_5_a7,
     author = {L. Gori and L. Pezza},
     title = {On some applications of the wavelet {Galerkin} method for boundary value problems},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {61--70},
     publisher = {mathdoc},
     volume = {15},
     number = {5},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2003_15_5_a7/}
}
TY  - JOUR
AU  - L. Gori
AU  - L. Pezza
TI  - On some applications of the wavelet Galerkin method for boundary value problems
JO  - Matematičeskoe modelirovanie
PY  - 2003
SP  - 61
EP  - 70
VL  - 15
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2003_15_5_a7/
LA  - ru
ID  - MM_2003_15_5_a7
ER  - 
%0 Journal Article
%A L. Gori
%A L. Pezza
%T On some applications of the wavelet Galerkin method for boundary value problems
%J Matematičeskoe modelirovanie
%D 2003
%P 61-70
%V 15
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2003_15_5_a7/
%G ru
%F MM_2003_15_5_a7
L. Gori; L. Pezza. On some applications of the wavelet Galerkin method for boundary value problems. Matematičeskoe modelirovanie, Tome 15 (2003) no. 5, pp. 61-70. http://geodesic.mathdoc.fr/item/MM_2003_15_5_a7/

[1] C. Canuto, A. Tabacco, K. Urban, “The wavelet element method. Part I: Construction and analysis”, Appl. Comput. Harmon. Anal., 6 (1999), 1–52 | DOI | MR | Zbl

[2] S. Bertoluzza, G. Naldi, J. C. Ravel, “Wavelet methods for the numerical solution of boundary value problems on the interval”, Theory, Algorithms and Applications, 7, eds. C. K. Chui, L. Montefusco, L. Puccio, Academic Press, 1994 | MR

[3] A. Cohen, I. Daubechies, P. Vial, “Wavelets on the interval and fast wavelet transforms”, Appl. and Comp. Harmonic Anal., 1:1 (1993), 54–81 | DOI | MR | Zbl

[4] W. Dahmen, “Wavelet and multiscale methods for operator equations”, Acta Numer., 6 (1997), 55–228 | DOI | MR | Zbl

[5] W. Dahmen, C. A. Micchelli, “Using the refinement equation for evaluating integrals of wavelets”, SIAM J. Numer. Anal., 30 (1993), 507–537 | DOI | MR | Zbl

[6] J. Fröhlich, K. Schneider, “An adaptive wavelet-vaguelette algorithm for the solution of PDEs”, J. Comput. Phys., 130 (1997), 174–190 | DOI | MR | Zbl

[7] R. Glowinski, W. Lawton, M. Ravachol, E. Tenenbaum, “Wavelet solutions of linear and nonlinear elliptic, parabolic and hyperbolic problems in one space dimension”, Computing Methods in Applied Science and Engineering, eds. R. Glowinski, A. Lichnewsky, SIAM, Philadelphia, PA, 1990, 55–120 | MR

[8] L. Gori, F. Pitolli, “Multiresolution analysis based on certain compactly supported refinable functions”, Approximation and Optimization (Cluj-Napoca, 1996), eds. G. Coman, W. W. Breckner, P. Blaga, Transilvania Press, 1997, 81–90 | MR | Zbl

[9] L. Gori, F. Pitolli, “A class of totally positive refinable functions”, Rend. Mat. Appl. Ser. 7, 20, (2000), 305–322 | MR | Zbl

[10] L. Gori, F. Pitolli, Refinable functions and positive operators, submitted

[11] L. Gori, F. Pitolli, L. Pezza, On the wavelet Galerkin method based on a particular class of wavelets, submitted

[12] M. L. Lo Cascio, F. Pitolli, “Generalized cardinal interpolation by refinable functions: some numerical results”, Note di Matematica, 15 (1995), 191–201 | MR | Zbl

[13] A. K. Louis, P. Maass, A. Rieder, Wavelet. Theory and Applications, Teubner Studienbücher Mathematik, Teubner, Stuttgart, 1998 | MR | Zbl

[14] Y. Meyer, “Ondelettes sur l'intervalle”, Rev. Mat. Iberoamericana, 7 (1992), 115–133 | MR

[15] F. Pitolli, “Refinement masks of Hurwitz type in the cardinal interpolation problem”, Rend. Mat. Appl. Ser. 7, 18 (1998), 549–563 | MR | Zbl

[16] A. Quarteroni, A. Valli, Numerical approximation of partial differential equations, Springer-Verlag, Berlin, 1994 | MR | Zbl