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Volumn 6, Issue C, 1997, Pages 137-197

An adaptive pseudo-wavelet approach for solving nonlinear partial differential equations

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EID: 0041981841     PISSN: 1874608X     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1874-608X(97)80006-4     Document Type: Chapter
Times cited : (36)

References (37)
  • 2
    • 0000139676 scopus 로고
    • 2 for the sparse representation of integral operators
    • 2 for the sparse representation of integral operators. SIAM J. Math. Anal. 24 (1993) 246-262
    • (1993) SIAM J. Math. Anal. , vol.24 , pp. 246-262
    • Alpert, B.1
  • 3
    • 0000139676 scopus 로고
    • Wavelet-like bases for the fast solution of second-kind integral equations
    • Alpert B., Beylkin G., Coifman R.R., and Rokhlin V. Wavelet-like bases for the fast solution of second-kind integral equations. SIAM J. Sci. Comput. 14 (1993) 159-184
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 159-184
    • Alpert, B.1    Beylkin, G.2    Coifman, R.R.3    Rokhlin, V.4
  • 5
    • 0026995365 scopus 로고
    • On the representation of operators in bases of compactly supported wavelets
    • Beylkin G. On the representation of operators in bases of compactly supported wavelets. SIAM J. Numer. Anal. 29 (1992) 1716-1740
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 1716-1740
    • Beylkin, G.1
  • 6
    • 20444506234 scopus 로고
    • On the fast algorithm for multiplication of functions in the wavelet bases
    • Meyer Y., and Roques S. (Eds), Editions Frontiéres, Philadelphia, PA
    • Beylkin G. On the fast algorithm for multiplication of functions in the wavelet bases. In: Meyer Y., and Roques S. (Eds). Proc. Int. Conf. "Wavelets and Applications," Toulouse 1992 (1993), Editions Frontiéres, Philadelphia, PA 53-61
    • (1993) Proc. Int. Conf. "Wavelets and Applications," Toulouse 1992 , pp. 53-61
    • Beylkin, G.1
  • 7
    • 0001894316 scopus 로고
    • Wavelets and fast numerical algorithms
    • Beylkin G. Wavelets and fast numerical algorithms. Proc. Sympos. Appl. Math. 47 (1993) 89-111
    • (1993) Proc. Sympos. Appl. Math. , vol.47 , pp. 89-111
    • Beylkin, G.1
  • 9
    • 0003100434 scopus 로고
    • Beylkin G., Coifman R., Daubechies I., Mallat S., Meyer Y., Raphael L., and Ruskai M.B. (Eds), Jones and Bartlett, Paris
    • Beylkin G., Coifman R.R., and Rokhlin V. Wavelets and Their Applications. In: Beylkin G., Coifman R., Daubechies I., Mallat S., Meyer Y., Raphael L., and Ruskai M.B. (Eds) (1992), Jones and Bartlett, Paris 181-210
    • (1992) Wavelets and Their Applications , pp. 181-210
    • Beylkin, G.1    Coifman, R.R.2    Rokhlin, V.3
  • 10
    • 77957154342 scopus 로고
    • Unpublished manuscript
    • Beylkin, G., and W. Hereman. Unpublished manuscript (1994).
    • (1994)
    • Beylkin, G.1    Hereman, W.2
  • 11
    • 77957113948 scopus 로고    scopus 로고
    • On the adaptive numerical solution of nonlinear partial differential equations in wavelet bases
    • to appear
    • to appear. Beylkin G., and Keiser J.M. On the adaptive numerical solution of nonlinear partial differential equations in wavelet bases. J. Comput. Phys. (1996)
    • (1996) J. Comput. Phys.
    • Beylkin, G.1    Keiser, J.M.2
  • 12
    • 77957123992 scopus 로고    scopus 로고
    • A new class of stable time discretization schemes for the solution of nonlinear PDEs
    • Beylkin G., Keiser J.M., and Vozovoi L. A new class of stable time discretization schemes for the solution of nonlinear PDEs. Preprint (1996)
    • (1996) Preprint
    • Beylkin, G.1    Keiser, J.M.2    Vozovoi, L.3
  • 13
    • 0001191104 scopus 로고
    • Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non-linéaires
    • Bony J.M. Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non-linéaires. Ann. Sci. École Norm. Sup. (4) 14 (1981) 209-246
    • (1981) Ann. Sci. École Norm. Sup. (4) , vol.14 , pp. 209-246
    • Bony, J.M.1
  • 14
    • 84966234195 scopus 로고
    • Parallel multilevel preconditioners
    • Bramble J.H., Pasciak J.E., and Xu J. Parallel multilevel preconditioners. Math. Comp. 55 (1990) 1-22
    • (1990) Math. Comp. , vol.55 , pp. 1-22
    • Bramble, J.H.1    Pasciak, J.E.2    Xu, J.3
  • 15
    • 77956834067 scopus 로고
    • A mathematical model illustrating the theory of turbulence
    • Burgers J.M. A mathematical model illustrating the theory of turbulence. Adv. Appl. Mech. 1 (1948) 171
    • (1948) Adv. Appl. Mech. , vol.1 , pp. 171
    • Burgers, J.M.1
  • 17
    • 0000332692 scopus 로고
    • On a quasilinear parabolic equation occurring in aerodynamics
    • Cole J.D. On a quasilinear parabolic equation occurring in aerodynamics. Quart. Appl. Math. 9 (1951) 225
    • (1951) Quart. Appl. Math. , vol.9 , pp. 225
    • Cole, J.D.1
  • 18
    • 84990556249 scopus 로고
    • A simple one-dimensional model for the three-dimensional vorticity equation
    • Constantin P., Lax P.D., and Majda A. A simple one-dimensional model for the three-dimensional vorticity equation. Comm. Pure Appl. Math. 38 (1985) 715
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 715
    • Constantin, P.1    Lax, P.D.2    Majda, A.3
  • 20
    • 33845592412 scopus 로고
    • Multilevel preconditioning
    • Dahmen W., and Kunoth A. Multilevel preconditioning. Numer. Math. 63 (1992) 315-344
    • (1992) Numer. Math. , vol.63 , pp. 315-344
    • Dahmen, W.1    Kunoth, A.2
  • 21
    • 84990575058 scopus 로고
    • Orthonormal bases of compactly supported wavelets
    • Daubechies I. Orthonormal bases of compactly supported wavelets. Comm. Pure Appl. Math. 41 (1988) 909-996
    • (1988) Comm. Pure Appl. Math. , vol.41 , pp. 909-996
    • Daubechies, I.1
  • 23
    • 0016555995 scopus 로고
    • On a Fourier method for the integration of hyperbolic equations
    • Fornberg B. On a Fourier method for the integration of hyperbolic equations. SIAM J. Numer. Anal. 12 (1975) 509
    • (1975) SIAM J. Numer. Anal. , vol.12 , pp. 509
    • Fornberg, B.1
  • 24
    • 0017901962 scopus 로고
    • A numerical and theoretical study of certain nonlinear wave phenomena
    • Fornberg B., and Whitham G.B. A numerical and theoretical study of certain nonlinear wave phenomena. Philos. Trans. Roy. Soc. London Ser. A 289 (1978) 373
    • (1978) Philos. Trans. Roy. Soc. London Ser. A , vol.289 , pp. 373
    • Fornberg, B.1    Whitham, G.B.2
  • 25
    • 0010807328 scopus 로고    scopus 로고
    • Wavelets and numerical split-step method: A global adaptive scheme
    • to appear
    • Gagnon, L. and J. M. Lina, Wavelets and numerical split-step method: a global adaptive scheme, J. Opt. Soc. Amer. B, to appear.
    • J. Opt. Soc. Amer. B
    • Gagnon, L.1    Lina, J.M.2
  • 26
    • 34250967631 scopus 로고
    • Zur Theorie der orthogonalen Funktionensysteme
    • Haar A. Zur Theorie der orthogonalen Funktionensysteme. Math. Ann. (1910) 331-371
    • (1910) Math. Ann. , pp. 331-371
    • Haar, A.1
  • 28
    • 0026909957 scopus 로고
    • Wavelet methods for fast resolution of elliptic problems
    • Jaffard S. Wavelet methods for fast resolution of elliptic problems. SIAM J. Numer. Anal. 29 (1992) 965-986
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 965-986
    • Jaffard, S.1
  • 29
    • 0040710255 scopus 로고
    • Numerical resolution of nonlinear partial differential equations using the wavelet approach
    • Beylkin G., Coifman R., Daubechies I., Mallat S., Meyer Y., Raphael L., and Ruskai M.B. (Eds), Jones and Bartlett, Philadelphia, PA
    • Liandrat J., Perrier V., and Tchamitchian P. Numerical resolution of nonlinear partial differential equations using the wavelet approach. In: Beylkin G., Coifman R., Daubechies I., Mallat S., Meyer Y., Raphael L., and Ruskai M.B. (Eds). Wavelets and Their Applications (1992), Jones and Bartlett, Philadelphia, PA 227-238
    • (1992) Wavelets and Their Applications , pp. 227-238
    • Liandrat, J.1    Perrier, V.2    Tchamitchian, P.3
  • 30
    • 0004198869 scopus 로고
    • Cambridge Stud. Adv. Math., Cambridge Univ. Press, Cambridge
    • Meyer Y. Wavelets and Operators (1992), Cambridge Stud. Adv. Math., Cambridge Univ. Press, Cambridge
    • (1992) Wavelets and Operators
    • Meyer, Y.1
  • 31
    • 77957106750 scopus 로고    scopus 로고
    • Le calcul scientifique, les ondelettes et les filtres miroirs en quadrature, Centre de Recherche de Mathématiques de la Décision
    • Report 9007
    • Meyer, Y., Le calcul scientifique, les ondelettes et les filtres miroirs en quadrature, Centre de Recherche de Mathématiques de la Décision, Report 9007.
    • Meyer, Y.1
  • 34
    • 0011691230 scopus 로고
    • Using wavelets to solve the Burgers' equation: A comparative study
    • Schult R.L., and Wyld H.W. Using wavelets to solve the Burgers' equation: A comparative study. Phys. Rev. A 46 (1992) 12
    • (1992) Phys. Rev. A , vol.46 , pp. 12
    • Schult, R.L.1    Wyld, H.W.2


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