Wavelet-Galerkin solutions for differential equations. (English) Zbl 0931.65082

A wavelet-Galerkin method applied to the numerical solution of boundary value problems and boundary layer problems for ordinary differential equations is presented. The application of wavelet analysis is demonstrated on two examples.


65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
Full Text: DOI


[1] Daubechies, I., Orthonormal bases of compactly supported wavelets, Comm Pure and Appl Math, 41, 909-996 (1988) · Zbl 0644.42026
[2] Mallat, S., A theory for multiresolution signal decomposition: the wavelet representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, 7, 674-693 (1989) · Zbl 0709.94650
[3] Mallat, S.; Lianghuang, Wen, Singularity detect and procesing with wavelets, IEEE Transaction on Information Theory, 38, 2, 617-643 (1992)
[4] Xuming, Yi; Biquan, Ye, Estimate of singularity order with wavelet numerical method, J of Guizhou University of Technology, 26, S1, 94-97 (1997)
[5] Lazaar, S.; Ponenti, P. J., Wavelet algorithms for numerical resolution of partial differential equations, Computer Methods in Applied Mechanics and Engineering, 116, 1, 309-314 (1994) · Zbl 0820.65059
[6] Xuming, Yi; Biquan, Ye; jianhua, Sun, Numerical Detection of boundary layer with wavelet, J of Wuhan University (Natural Science Edition), 44, 1, 24-28 (1998) · Zbl 0921.65055
[7] Beylkin, G., On the representation of operators in bases of compactly supported wavelets, SIAM, J of Numerical Analsis, 29, 1716-1740 (1992) · Zbl 0766.65007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.