메뉴 건너뛰기




Volumn 234, Issue , 2014, Pages 267-276

Legendre wavelets method for solving fractional partial differential equations with Dirichlet boundary conditions

Author keywords

Fractional partial differential equations; Operational matrices; Two dimensional Legendre wavelets

Indexed keywords

BOUNDARY CONDITIONS; TWO DIMENSIONAL;

EID: 84896512243     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2014.02.047     Document Type: Article
Times cited : (126)

References (31)
  • 1
    • 84865372389 scopus 로고    scopus 로고
    • Error analysis for numerical solution of fractional differential equation by haar wavelets method
    • Y. Chen, and M.Y.C. Yu Error analysis for numerical solution of fractional differential equation by haar wavelets method J. Comput. Sci. 3 5 2012 367 373
    • (2012) J. Comput. Sci. , vol.3 , Issue.5 , pp. 367-373
    • Chen, Y.1    Yu, M.Y.C.2
  • 2
    • 77956412154 scopus 로고    scopus 로고
    • Analysis of stability and convergence of numerical approximation for the Riesz fractional reaction-dispersion equation
    • J. Chen Analysis of stability and convergence of numerical approximation for the Riesz fractional reaction-dispersion equation J. Xiamen Univ. (Nat. Sci.) 46 5 2007 616 619
    • (2007) J. Xiamen Univ. (Nat. Sci.) , vol.46 , Issue.5 , pp. 616-619
    • Chen, J.1
  • 3
    • 1542425102 scopus 로고    scopus 로고
    • Numerical solution of the space fractional Fokker-Planck equation
    • F. Liu, V. Anh, and I. Turner Numerical solution of the space fractional Fokker-Planck equation J. Comput. Appl. Math. 166 1 2004 209 219
    • (2004) J. Comput. Appl. Math. , vol.166 , Issue.1 , pp. 209-219
    • Liu, F.1    Anh, V.2    Turner, I.3
  • 4
    • 51749116733 scopus 로고    scopus 로고
    • Finite difference approximations for the fractional Fokker Planck equation
    • S. Chen, and F. Liu Finite difference approximations for the fractional Fokker Planck equation Appl. Math. Modell. 33 1 2009 256 273
    • (2009) Appl. Math. Modell. , vol.33 , Issue.1 , pp. 256-273
    • Chen, S.1    Liu, F.2
  • 5
    • 0007042083 scopus 로고    scopus 로고
    • Nonlinear oscillation with fractional derivative and its applications
    • J. He Nonlinear oscillation with fractional derivative and its applications Int. Conf. Vibr. Eng. 98 1998 288 291
    • (1998) Int. Conf. Vibr. Eng. , vol.98 , pp. 288-291
    • He, J.1
  • 6
    • 0347763940 scopus 로고    scopus 로고
    • Some applications of nonlinear fractional differential equations and their approximations
    • J. He Some applications of nonlinear fractional differential equations and their approximations Bull. Sci. Technol. 15 2 1999 86 90
    • (1999) Bull. Sci. Technol. , vol.15 , Issue.2 , pp. 86-90
    • He, J.1
  • 7
    • 0001983732 scopus 로고    scopus 로고
    • Fractional calculus: Some basic problems in continuum and statistical mechanics
    • F. Mainardi Fractional calculus: some basic problems in continuum and statistical mechanics Fract. Fract. Calculus Contin. Mech. 1997 291 348
    • (1997) Fract. Fract. Calculus Contin. Mech. , pp. 291-348
    • Mainardi, F.1
  • 8
    • 33745739434 scopus 로고    scopus 로고
    • Fractional generalized splines and signal processing
    • R. Panda, and M. Dash Fractional generalized splines and signal processing Signal Process 86 2006 2340 2350
    • (2006) Signal Process , vol.86 , pp. 2340-2350
    • Panda, R.1    Dash, M.2
  • 9
    • 52349114093 scopus 로고    scopus 로고
    • Analog fractional order controller in temperature and motor control applications
    • G. Bohannan Analog fractional order controller in temperature and motor control applications J. Vibr. Control 14 2008 1487 1498
    • (2008) J. Vibr. Control , vol.14 , pp. 1487-1498
    • Bohannan, G.1
  • 10
    • 20444465327 scopus 로고    scopus 로고
    • Fractional dynamics of interfaces between soft-nanoparticles and rough substrates
    • T. Chow Fractional dynamics of interfaces between soft-nanoparticles and rough substrates Phys. Lett. A 342 2005 148 155
    • (2005) Phys. Lett. A , vol.342 , pp. 148-155
    • Chow, T.1
  • 11
    • 84855814332 scopus 로고    scopus 로고
    • Chebyshev wavelets approach for nonlinear systems of volterra integral equations
    • J. Biazar, and H. Ebrahimi Chebyshev wavelets approach for nonlinear systems of volterra integral equations Comput. Math. Appl. 63 2012 608 616
    • (2012) Comput. Math. Appl. , vol.63 , pp. 608-616
    • Biazar, J.1    Ebrahimi, H.2
  • 12
    • 84884153266 scopus 로고    scopus 로고
    • Wavelets method for solving systems of nonlinear singular fractional volterra integro-differential equations
    • M.H. Heydari, M.R. Hooshmandasl, F. Mohammadi, and C. Cattani Wavelets method for solving systems of nonlinear singular fractional volterra integro-differential equations Commun. Nonlinear Sci. Numer. Simul. 19 1 2014 37 48
    • (2014) Commun. Nonlinear Sci. Numer. Simul. , vol.19 , Issue.1 , pp. 37-48
    • Heydari, M.H.1    Hooshmandasl, M.R.2    Mohammadi, F.3    Cattani, C.4
  • 14
    • 0035323556 scopus 로고    scopus 로고
    • Legendre wavelets operational matrix of integration
    • M. Razzaghi, and S. Yousefi Legendre wavelets operational matrix of integration Int. J. Sys. Sci. 32 4 2001 495 502
    • (2001) Int. J. Sys. Sci. , vol.32 , Issue.4 , pp. 495-502
    • Razzaghi, M.1    Yousefi, S.2
  • 15
    • 84881272856 scopus 로고    scopus 로고
    • Wavelets and their application for the solution of Poissons and Schrödingers equation
    • S. Goedecker Wavelets and their application for the solution of Poissons and Schrödingers equation Multi. Simul. Methods Mol. Sci. 42 2009 507 534
    • (2009) Multi. Simul. Methods Mol. Sci. , vol.42 , pp. 507-534
    • Goedecker, S.1
  • 17
    • 70449534671 scopus 로고    scopus 로고
    • A study of multiscale wavelet-based elements for adaptive finite element analysis
    • X. Chen, J. Xiang, B. Li, and Z. He A study of multiscale wavelet-based elements for adaptive finite element analysis Adv. Eng. Softw 41 2010 196 205
    • (2010) Adv. Eng. Softw , vol.41 , pp. 196-205
    • Chen, X.1    Xiang, J.2    Li, B.3    He, Z.4
  • 18
    • 64849115449 scopus 로고    scopus 로고
    • Haar wavelet method for solving Fishers equation
    • G. Hariharan, K. Kannan, and K. Sharma Haar wavelet method for solving Fishers equation Appl. Math. Comput. 211 2 2009 284 292
    • (2009) Appl. Math. Comput. , vol.211 , Issue.2 , pp. 284-292
    • Hariharan, G.1    Kannan, K.2    Sharma, K.3
  • 19
    • 33947638928 scopus 로고    scopus 로고
    • From two-dimensional nonlinear diffusion to coupled Haar wavelet shrinkage
    • P. Mrazek, and J. Weickert From two-dimensional nonlinear diffusion to coupled Haar wavelet shrinkage J. Vis. Commun. Image. Representation 18 2007 162 175
    • (2007) J. Vis. Commun. Image. Representation , vol.18 , pp. 162-175
    • Mrazek, P.1    Weickert, J.2
  • 20
    • 0141795403 scopus 로고    scopus 로고
    • Adaptive multiscale wavelet-galerkin analysis for plane elasticity problems and its application to multiscale topology design optimation
    • (Comput. Appl. Math.)
    • J.E. Kim, G.-W. Yang, and Y.Y. Kim Adaptive multiscale wavelet-galerkin analysis for plane elasticity problems and its application to multiscale topology design optimation Int. J. Solids Struct. 40 2003 6473 6496 (Comput. Appl. Math.)
    • (2003) Int. J. Solids Struct. , vol.40 , pp. 6473-6496
    • Kim, J.E.1    Yang, G.-W.2    Kim, Y.Y.3
  • 21
    • 65449142896 scopus 로고    scopus 로고
    • Three-dimensional analysis of functionally graded plate based on the Haar wavelet method
    • Z. Chun, and Z. Zheng Three-dimensional analysis of functionally graded plate based on the Haar wavelet method Acta Mech. Solida Sin. 20 2 2007 95 102
    • (2007) Acta Mech. Solida Sin. , vol.20 , Issue.2 , pp. 95-102
    • Chun, Z.1    Zheng, Z.2
  • 22
    • 64849088409 scopus 로고    scopus 로고
    • Weak formulation based haar wavelet method for solving differential equations
    • J. Majak, M. Pohlak, M. Eerme, and T. Lepikult Weak formulation based haar wavelet method for solving differential equations Appl. Math. Comput. 211 2009 488 494
    • (2009) Appl. Math. Comput. , vol.211 , pp. 488-494
    • Majak, J.1    Pohlak, M.2    Eerme, M.3    Lepikult, T.4
  • 23
    • 77950368621 scopus 로고    scopus 로고
    • A wavelet collocation method for the static analysis of sandwich plates using a layerwise theory
    • L.M.S. Castro, A. Ferreira, S. Bertoluzza, R. Patra, and J. Reddy A wavelet collocation method for the static analysis of sandwich plates using a layerwise theory Compos. Struct. 92 2010 1786 1792
    • (2010) Compos. Struct. , vol.92 , pp. 1786-1792
    • Castro, L.M.S.1    Ferreira, A.2    Bertoluzza, S.3    Patra, R.4    Reddy, J.5
  • 24
    • 84870255744 scopus 로고    scopus 로고
    • Wavelets collocation methods for the numerical solution of elliptic boundary problems
    • I. Aziz, S. ul Islam, and B. Sarler Wavelets collocation methods for the numerical solution of elliptic boundary problems Appl. Math. Modell. 37 2013 676 694
    • (2013) Appl. Math. Modell. , vol.37 , pp. 676-694
    • Aziz, I.1    Ul Islam, S.2    Sarler, B.3
  • 25
    • 84881283092 scopus 로고    scopus 로고
    • Two-dimensional Legendre wavelets for solving fractional poisson equation with Dirichlet boundary conditions
    • M.H. Heydari, M.R. Hooshmandasl, F.M.M. Ghaini, and F. Fereidouni Two-dimensional Legendre wavelets for solving fractional poisson equation with Dirichlet boundary conditions Eng. Anal. Boundary Elem. 37 2013 1331 1338
    • (2013) Eng. Anal. Boundary Elem. , vol.37 , pp. 1331-1338
    • Heydari, M.H.1    Hooshmandasl, M.R.2    Ghaini, F.M.M.3    Fereidouni, F.4
  • 28
    • 84966210236 scopus 로고
    • Multiresolution approximation and wavelets
    • S. Mallat Multiresolution approximation and wavelets Trans. Am. Math. Soc 315 1989 69 89
    • (1989) Trans. Am. Math. Soc , vol.315 , pp. 69-89
    • Mallat, S.1
  • 29
    • 84858110986 scopus 로고    scopus 로고
    • Wavelet collocation method for solving multi order fractional differential equations
    • Article ID 542401, 19 pages
    • M.H. Heydari, M.R. Hooshmandasl, F.M.M. Ghaini, and F. Mohammadi Wavelet collocation method for solving multi order fractional differential equations J. Appl. Math. 2012 2012 Article ID 542401, 19 pages, http://dx.doi.org/10.1155/ 2012/542401
    • (2012) J. Appl. Math. , vol.2012
    • Heydari, M.H.1    Hooshmandasl, M.R.2    Ghaini, F.M.M.3    Mohammadi, F.4
  • 30
    • 34247336205 scopus 로고    scopus 로고
    • Kronecker operational matrices for fractional calculus and some applications
    • A. Kilicman, and Z.A. Zhour Kronecker operational matrices for fractional calculus and some applications Appl. Math. Comput. 187 1 2007 250 265
    • (2007) Appl. Math. Comput. , vol.187 , Issue.1 , pp. 250-265
    • Kilicman, A.1    Zhour, Z.A.2
  • 31
    • 73449118638 scopus 로고    scopus 로고
    • Legendre wavelet method for numerical solutions of partial differential equations
    • L. Nanshan, and E.B. Lin Legendre wavelet method for numerical solutions of partial differential equations Numer. Methods Partial Differ. Equ. 26 1 2010 81 94
    • (2010) Numer. Methods Partial Differ. Equ. , vol.26 , Issue.1 , pp. 81-94
    • Nanshan, L.1    Lin, E.B.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.