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Volumn 56, Issue 1, 2007, Pages 28-46

Application of the Haar wavelet transform to solving integral and differential equations

Author keywords

Collocation method; Evolution equations; Haar wavelet method; Integral equations; Sine Gordon equation

Indexed keywords


EID: 34247369315     PISSN: 14060086     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (141)

References (40)
  • 1
    • 84990575058 scopus 로고
    • Orthonormal bases of compactly supported wavelets
    • Daubechies, I. Orthonormal bases of compactly supported wavelets. Comm. Pure Appl. Math., 1988, 41, 909-996.
    • (1988) Comm. Pure Appl. Math , vol.41 , pp. 909-996
    • Daubechies, I.1
  • 2
    • 0030242748 scopus 로고    scopus 로고
    • The computation of wavelet - Galerkin approximation on a bounded interval
    • Chen, M.-Q., Hwang, C. and Shin, Y.-P. The computation of wavelet - Galerkin approximation on a bounded interval. Int. J. Numer. Methods Eng., 1996, 39, 2921-2944.
    • (1996) Int. J. Numer. Methods Eng , vol.39 , pp. 2921-2944
    • Chen, M.-Q.1    Hwang, C.2    Shin, Y.-P.3
  • 5
    • 0032204081 scopus 로고    scopus 로고
    • A wavelet-optimized, very much order adaptive grid and order numerical method
    • Jameson, L. A wavelet-optimized, very much order adaptive grid and order numerical method. SIAM J. Sci. Comput., 1998, 19, 1980-2013.
    • (1998) SIAM J. Sci. Comput , vol.19 , pp. 1980-2013
    • Jameson, L.1
  • 6
    • 0036335260 scopus 로고    scopus 로고
    • The Haar wavelet transform: Its status and achievements
    • Stanković, R. S. and Falkowski, B. J. The Haar wavelet transform: its status and achievements. Comput. Electr. Eng., 2003, 29, 25-44.
    • (2003) Comput. Electr. Eng , vol.29 , pp. 25-44
    • Stanković, R.S.1    Falkowski, B.J.2
  • 8
    • 17444389881 scopus 로고    scopus 로고
    • Haar wavelets based technique in evolution problems
    • Cattani, C. Haar wavelets based technique in evolution problems. Proc. Estonian Acad. Sci. Phys. Math., 2004, 53, 45-65.
    • (2004) Proc. Estonian Acad. Sci. Phys. Math , vol.53 , pp. 45-65
    • Cattani, C.1
  • 9
    • 0030649749 scopus 로고    scopus 로고
    • Haar wavelet method for solving lumped and distributed-parameter systems
    • Chen, C. F. and Hsiao, C.-H. Haar wavelet method for solving lumped and distributed-parameter systems. IEE Proc. Control Theory Appl., 1997, 144, 87-94.
    • (1997) IEE Proc. Control Theory Appl , vol.144 , pp. 87-94
    • Chen, C.F.1    Hsiao, C.-H.2
  • 10
    • 0033084472 scopus 로고    scopus 로고
    • Wavelet approach to optimising dynamic systems
    • Chen, C. F. and Hsiao, C.-H. Wavelet approach to optimising dynamic systems. IEE Proc. Control Theory Appl., 1997, 146, 213-219.
    • (1997) IEE Proc. Control Theory Appl , vol.146 , pp. 213-219
    • Chen, C.F.1    Hsiao, C.-H.2
  • 11
    • 0003851590 scopus 로고    scopus 로고
    • State analysis of time-varying singular bilinear systems via Haar wavelets
    • Hsiao, C.-H. and Wang, W.-J. State analysis of time-varying singular bilinear systems via Haar wavelets. Math. Comput. Simul., 2000, 52, 11-20.
    • (2000) Math. Comput. Simul , vol.52 , pp. 11-20
    • Hsiao, C.-H.1    Wang, W.-J.2
  • 12
    • 0003778082 scopus 로고    scopus 로고
    • State analysis of time-varying singular nonlinear systems via Haar wavelets
    • Hsiao, C.-H. and Wang, W.-J. State analysis of time-varying singular nonlinear systems via Haar wavelets. Math. Comput. Simul., 1999, 51, 91-100.
    • (1999) Math. Comput. Simul , vol.51 , pp. 91-100
    • Hsiao, C.-H.1    Wang, W.-J.2
  • 13
    • 0034857840 scopus 로고    scopus 로고
    • Haar wavelet approach to nonlinear stiff systems
    • Hsiao, C.-H. and Wang, W.-J. Haar wavelet approach to nonlinear stiff systems. Math. Comput. Simul., 2001, 57, 347-353.
    • (2001) Math. Comput. Simul , vol.57 , pp. 347-353
    • Hsiao, C.-H.1    Wang, W.-J.2
  • 14
    • 1242276102 scopus 로고    scopus 로고
    • Haar wavelet direct method for solving variational problems
    • Hsiao, C.-H. Haar wavelet direct method for solving variational problems. Math. Comput. Simul., 2004, 64, 569-585.
    • (2004) Math. Comput. Simul , vol.64 , pp. 569-585
    • Hsiao, C.-H.1
  • 15
    • 0141514730 scopus 로고    scopus 로고
    • Wavelet collocation methods for a first kind boundary integral equation in acoustic scattering
    • b 17, 281-308
    • Hsiao, G.-C. and Rathsfeld, A. Wavelet collocation methods for a first kind boundary integral equation in acoustic scattering. Adv. Comput. Math., 2002, b 17, 281-308.
    • (2002) Adv. Comput. Math
    • Hsiao, G.-C.1    Rathsfeld, A.2
  • 16
    • 0000139676 scopus 로고
    • Wavelet-like bases for the fast solution of second-kind integral equations
    • Alpert, B., Beylkin, G., Coifman, R. and Rokhlin, V. Wavelet-like bases for the fast solution of second-kind integral equations. SIAM J. Sci. Comput., 1993, 14, 159-184.
    • (1993) SIAM J. Sci. Comput , vol.14 , pp. 159-184
    • Alpert, B.1    Beylkin, G.2    Coifman, R.3    Rokhlin, V.4
  • 17
    • 14044257796 scopus 로고    scopus 로고
    • Fast solvers of integral equations of the second kind: Wavelet methods
    • Vainikko, G., Kivinukk, A. and Lippus, J. Fast solvers of integral equations of the second kind: wavelet methods. J. Complexity, 2005, 21, 243-273.
    • (2005) J. Complexity , vol.21 , pp. 243-273
    • Vainikko, G.1    Kivinukk, A.2    Lippus, J.3
  • 18
    • 23744472619 scopus 로고    scopus 로고
    • Legendre wavelets method for the nonlinear Volterra-Fredholm integral equations
    • Yousefi, S. and Razzaghi, M. Legendre wavelets method for the nonlinear Volterra-Fredholm integral equations. Math. Comput. Simul., 2005, 70, 1-8.
    • (2005) Math. Comput. Simul , vol.70 , pp. 1-8
    • Yousefi, S.1    Razzaghi, M.2
  • 19
    • 33747588293 scopus 로고    scopus 로고
    • Numerical solution of Fredholm integral equation of the first kind with collocation method and estimation of error bound
    • Maleknejad, K., Aghazadeh, N. and Molapourasl, F. Numerical solution of Fredholm integral equation of the first kind with collocation method and estimation of error bound. Appl. Math. Comput., 2006, 179, 352-359.
    • (2006) Appl. Math. Comput , vol.179 , pp. 352-359
    • Maleknejad, K.1    Aghazadeh, N.2    Molapourasl, F.3
  • 20
    • 33644929052 scopus 로고    scopus 로고
    • Solving second kind Fredholm integral equation by periodic wavelet Galerkin method
    • Xiao, J.-Y., Wen, L.-H. and Zhang, D. Solving second kind Fredholm integral equation by periodic wavelet Galerkin method. Appl. Math. Comput., 2006, 175, 508-518.
    • (2006) Appl. Math. Comput , vol.175 , pp. 508-518
    • Xiao, J.-Y.1    Wen, L.-H.2    Zhang, D.3
  • 21
    • 0037401557 scopus 로고    scopus 로고
    • Wavelet applications to the Petrov-Galerkin method for Hammerstein equations
    • Kaneko, H., Noren, R. D. and Novaprateep, B. Wavelet applications to the Petrov-Galerkin method for Hammerstein equations. Appl. Numer. Math., 2003, 45, 255-273.
    • (2003) Appl. Numer. Math , vol.45 , pp. 255-273
    • Kaneko, H.1    Noren, R.D.2    Novaprateep, B.3
  • 22
    • 31644436367 scopus 로고    scopus 로고
    • The collocation method for Hammerstein equations by Daubechies wavelets
    • Maleknejad, K. and Derili, H. The collocation method for Hammerstein equations by Daubechies wavelets. Appl. Math. Comput., 2006, 172, 846-864.
    • (2006) Appl. Math. Comput , vol.172 , pp. 846-864
    • Maleknejad, K.1    Derili, H.2
  • 23
    • 0034159354 scopus 로고    scopus 로고
    • Wavelet - Galerkin method for integro-differential equations
    • Avudainayagam, A. and Vano, C. Wavelet - Galerkin method for integro-differential equations. Appl. Numer. Math., 2000, 32, 247-254.
    • (2000) Appl. Numer. Math , vol.32 , pp. 247-254
    • Avudainayagam, A.1    Vano, C.2
  • 24
    • 18144375589 scopus 로고    scopus 로고
    • Wavelet method for solving integral equations of simple liquids
    • Fedorov, M. V. and Chyev, G. N. Wavelet method for solving integral equations of simple liquids. J. Mol. Liq., 2005, 120, 159-162.
    • (2005) J. Mol. Liq , vol.120 , pp. 159-162
    • Fedorov, M.V.1    Chyev, G.N.2
  • 25
    • 0035501470 scopus 로고    scopus 로고
    • Solving second kind integral equations by Galerkin methods with continuous orthogonal wavelets
    • Liang, X.-Z., Liu, M.-C. and Che, X.-J. Solving second kind integral equations by Galerkin methods with continuous orthogonal wavelets. J. Comput. Appl. Math., 2001, 136, 149-161.
    • (2001) J. Comput. Appl. Math , vol.136 , pp. 149-161
    • Liang, X.-Z.1    Liu, M.-C.2    Che, X.-J.3
  • 26
    • 25144494715 scopus 로고    scopus 로고
    • Wavelet Galerkin method for numerical solution of nonlinear integral equation
    • Mahmoudi, Y. Wavelet Galerkin method for numerical solution of nonlinear integral equation. Appl. Math. Comput., 2005, 167, 1119-1129.
    • (2005) Appl. Math. Comput , vol.167 , pp. 1119-1129
    • Mahmoudi, Y.1
  • 27
    • 31944442864 scopus 로고    scopus 로고
    • The linear Legendre mother wavelets operational matrix of integration and its application
    • Khellat, F. and Yousefi, S. A. The linear Legendre mother wavelets operational matrix of integration and its application. J. Franklin Inst., 2006, 143, 181-190.
    • (2006) J. Franklin Inst , vol.143 , pp. 181-190
    • Khellat, F.1    Yousefi, S.A.2
  • 28
    • 33644890784 scopus 로고    scopus 로고
    • Expansion method for linear integral equations by cardinal B-spline wavelet and Shannon wavelet bases to obtain Galerkin system
    • Maleknejad, K. and Lotfi, T. Expansion method for linear integral equations by cardinal B-spline wavelet and Shannon wavelet bases to obtain Galerkin system. Appl. Math. Comput., 2006, 175, 347-355.
    • (2006) Appl. Math. Comput , vol.175 , pp. 347-355
    • Maleknejad, K.1    Lotfi, T.2
  • 29
    • 25644439799 scopus 로고    scopus 로고
    • Numerical solution of non-linear Fredholm integral equations by using multiwavelets in the Petrov - Galerkin method
    • Maleknejad, K. and Karami, M. Numerical solution of non-linear Fredholm integral equations by using multiwavelets in the Petrov - Galerkin method. Appl. Math. Comput., 2005, 168, 102-110.
    • (2005) Appl. Math. Comput , vol.168 , pp. 102-110
    • Maleknejad, K.1    Karami, M.2
  • 31
    • 34247377717 scopus 로고    scopus 로고
    • Solution of nonlinear integral equations via the Haar wavelet method
    • Lepik, Ü. and Tamme, E. Solution of nonlinear integral equations via the Haar wavelet method. Proc. Estonian Acad. Sci. Phys. Math., 2007, 56, 17-27.
    • (2007) Proc. Estonian Acad. Sci. Phys. Math , vol.56 , pp. 17-27
    • Lepik, U.1    Tamme, E.2
  • 32
    • 33646152103 scopus 로고    scopus 로고
    • Haar wavelet method for non-linear integro-differential equations
    • Lepik, Ü. Haar wavelet method for non-linear integro-differential equations. Appl. Math. Comput., 2006, 176, 324-333.
    • (2006) Appl. Math. Comput , vol.176 , pp. 324-333
    • Lepik, U.1
  • 33
    • 9644294400 scopus 로고    scopus 로고
    • Using rationalized Haar wavelet for solving linear integral equations
    • Maleknejad, K. and Mirzaee, F. Using rationalized Haar wavelet for solving linear integral equations. Appl. Math. Comput., 2005, 160, 579-587.
    • (2005) Appl. Math. Comput , vol.160 , pp. 579-587
    • Maleknejad, K.1    Mirzaee, F.2
  • 34
    • 17444421176 scopus 로고    scopus 로고
    • Numerical solution of differential equations using Haar wavelets
    • Lepik, Ü. Numerical solution of differential equations using Haar wavelets. Math. Comput. Simul., 2003, 68, 127-143.
    • (2003) Math. Comput. Simul , vol.68 , pp. 127-143
    • Lepik, U.1
  • 35
    • 33846929829 scopus 로고    scopus 로고
    • Numerical solution of evolution equations by the Haar wavelet method
    • accepted
    • Lepik, Ü. Numerical solution of evolution equations by the Haar wavelet method. Appl. Math. Comput. (accepted).
    • Appl. Math. Comput
    • Lepik, U.1
  • 37
    • 32844468042 scopus 로고    scopus 로고
    • Nondestructive damage evaluation of plates using the multiresolution analysis of two-dimensional Haar wavelet
    • Kim, B. H., Kim, H. and Park, T. Nondestructive damage evaluation of plates using the multiresolution analysis of two-dimensional Haar wavelet. J. Sound Vibration, 2006, 292, 82-104.
    • (2006) J. Sound Vibration , vol.292 , pp. 82-104
    • Kim, B.H.1    Kim, H.2    Park, T.3
  • 38
    • 28444437361 scopus 로고    scopus 로고
    • Wavelet based preconditioners for sparse linear systems
    • Kumar, B. V. R. and Mehra, M. Wavelet based preconditioners for sparse linear systems. Appl. Math. Comput., 2005, 171, 203-224.
    • (2005) Appl. Math. Comput , vol.171 , pp. 203-224
    • Kumar, B.V.R.1    Mehra, M.2
  • 39
    • 32644436722 scopus 로고    scopus 로고
    • Wavelet analysis of dynamical systems
    • Cattani, C. Wavelet analysis of dynamical systems. Electron. Commun. (Kiev), 2002, 17, 115-124.
    • (2002) Electron. Commun. (Kiev) , vol.17 , pp. 115-124
    • Cattani, C.1
  • 40
    • 0035254608 scopus 로고    scopus 로고
    • Nonlinear response of the sine-Gordon breather to an a.c. driver
    • Forinash, K. and Willis, C. R. Nonlinear response of the sine-Gordon breather to an a.c. driver. Physica D, 2001, 149, 95-106.
    • (2001) Physica D , vol.149 , pp. 95-106
    • Forinash, K.1    Willis, C.R.2


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