zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Harmonic wavelets towards the solution of nonlinear PDE. (English) Zbl 1118.65133
The paper is dominated by the problem of generation of harmonic wavelets and their connection coefficients. Only at the end of the papers on just a single page the usual straight forward application of wavelets to initial value problems is sketched.

MSC:
65T60Wavelets (numerical methods)
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
35K55Nonlinear parabolic equations
WorldCat.org
Full Text: DOI
References:
[1] Fröhlich, J.; Schneider, K.: An adaptive wavelet Galerkin algorithm for one- and two-dimensional flame computations. Eur. J. Mech. B/fluids 13, No. 4, 439-471 (1994) · Zbl 0814.76068
[2] Goedecker, S.; Ivanov, O.: Solution of multiscale partial differential equations using wavelets. Computers in physic 16, No. 6, 548-555 (1998)
[3] Vasiliev, O. V.; Paolucci, S.; Sen, M.: A multilevel wavelet collocation method for solving partial differential equations in a finite domain. Journal of computational physics 120, 33-47 (1997) · Zbl 0837.65113
[4] Tchamitchian, P.: Wavelets and differential operators. Proceedings of symposia in applied mathematics 47, 77-88 (1993) · Zbl 0825.35007
[5] Lazaar, S.; Liandrat, J.; Tchamitchian, P.: Algorithme à base d’ondelettes pour la résolution numérique d’équations aux dérivés partielles à coefficents variables. CR acad. Sci. Paris 319, 1101-1194 (1994)
[6] Lazaar, S.; Ponenti, Pj.; Liandrat, J.; Tchamitchian, P.: Wavelet algorithms for numerical resolution of partial differential equations. Comput. methods appl. Mech. engrg. 116, 309-314 (1994) · Zbl 0820.65059
[7] Bacry, E.; Mallat, S.; Papanicolaou, G.: A wavelet based space-time numerical method for partial differential equations. Mathematical models numerical analysis 26, 417-438 (2004) · Zbl 0768.65062
[8] J. Baccou and J. Liandrat, Definition and analysis of a wavelet/fictitious domain solver for the 2D-heat equation on a general domain, Mathematical Models and Methods in Applied Sciences (to appear). · Zbl 1103.65105
[9] Chen, W. -S.; Lin, W.: Galerkin trigonometric wavelet methods for the natural boundary integral equations. Applied mathematics and computation 121, 75-92 (2001) · Zbl 1026.65111
[10] Micchelli, C. A.; Xu, Y.; Zhao, Y.: Wavelet Galerkin methods for second-kind integral equations. Journal of computational and applied mathematics 86, 251-270 (1997) · Zbl 0913.65129
[11] Kaneko, H.; Noren, R. D.; Novaprateep, B.: Wavelet applications to the Petrov-Galerkin method Hammerstein equation. Applied numerical mathematics 45, 255-273 (2003) · Zbl 1019.65106
[12] Shen, Y.; Lin, W.: The natural integral equations of plane elasticity and its wavelet methods. Applied mathematics and computation 150, 417-438 (2004) · Zbl 1059.74061
[13] Chen, Z.; Micchelli, C. A.; Xu, Y.: Discrete wavelet Petrov-Galerkin methods. Advances in computational mathematics 16, 1-28 (2002) · Zbl 0998.65120
[14] Avudainayagam, A.; Vani, C.: Wavelet-Galerkin method for integro-differential equations. Applied numerical mathematics 32, 247-254 (2000) · Zbl 0955.65100
[15] Dahmen, W.: Wavelet and multiscale methods for operator equations. Acta numerica 6, 55-228 (1997) · Zbl 0884.65106
[16] Bellomo, N.: Nonlinear models and problems in applied sciences from differential quadrature to generalized collocation methods. Mathl. comput. Modelling 26, No. 4, 13-34 (1997) · Zbl 0898.65074
[17] Bellomo, N.; Ridolfi, L.: Solution of nonlinear initial-boundary value problems by sinc collocation-interpolation methods. Computers math. Applic. 29, No. 4, 15-28 (1995) · Zbl 0822.65075
[18] Longo, E.; Teppati, G.; Bellomo, N.: Discretization of nonlinear models by sinc collocation-interpolation methods. Computers math. Applic. 32, No. 4, 65-81 (1996) · Zbl 0858.65104
[19] Newland, D. E.: Harmonic wavelet analysis. Proc. R. Soc. lond. A 443, 203-222 (1993) · Zbl 0793.42020
[20] Lin, E. B.; Zhou, X.: Connection coefficients on an interval and wavelet solutions of Burgers equation. Journal of computational and applied mathematics 135, 63-78 (2001) · Zbl 0990.65096
[21] Cattani, C.: The wavelets based technique in the dispersive wave propagation. International applied mechanics 39, No. 4, 132-140 (2003) · Zbl 1054.42022
[22] Cattani, C.: Harmonic wavelet solutions of the Schrödinger equation. International journal of fluid mechanics research 5, 1-10 (2003)
[23] Latto, A.; Resnikoff, H. L.; Tenenbaum, E.: The evaluation of connection coefficients of compactly supported wavelets. Proc. of the French-USA workshop on wavelets and turbulence, 76-89 (1992)
[24] Dahmen, W.; Micchelli, C. A.: Using the refinement equation for evaluating integrals of wavelets. SIAM J. Numer. anal. 30, 507-537 (1993) · Zbl 0773.65006
[25] Muniandy, S. V.; Moroz, I. M.: Galerkin modelling of the Burgers equation using harmonic wavelets. Phys. lett. A 235, 352-356 (1997) · Zbl 1044.65511
[26] Mouri, H.; Kubotani, H.: Real-valued harmonic wavelets. Phys. lett. A 201, 53-60 (1995) · Zbl 1020.42500
[27] Daubechies, I.: The lectures on wavelets. (1992) · Zbl 0776.42018
[28] Cattani, C.: Multiscale analysis of wave propagation in composite materials. Mathematical modelling and analysis 8, No. 4, 267-282 (2003) · Zbl 1109.74332
[29] Cattani, C.; Rushchitsky, J. J.: Solitary elastic waves and elastic wavelets. International applied mechanics 39, No. 6, 741-752 (2003)