메뉴 건너뛰기




Volumn 2013, Issue , 2013, Pages

Application of the local fractional series expansion method and the variational iteration method to the Helmholtz equation involving local fractional derivative operators

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84890038237     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2013/259125     Document Type: Article
Times cited : (39)

References (44)
  • 1
    • 36749114658 scopus 로고
    • Transmission problems for the Helmholtz equation
    • MR0495653 10.1063/1.523808 ZBL0433.35017
    • Kreß R., Roach G. F., Transmission problems for the Helmholtz equation. Journal of Mathematical Physics 1978 19 6 1433 1437 MR0495653 10.1063/1.523808 ZBL0433.35017
    • (1978) Journal of Mathematical Physics , vol.19 , Issue.6 , pp. 1433-1437
    • Kreß, R.1    Roach, G.F.2
  • 2
    • 0344549300 scopus 로고    scopus 로고
    • Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions
    • DOI 10.1002/(SICI)1097-0207(19991010)46:4 <471::AID-NME684>3.0. CO;2-6
    • Deraemaeker A., Babuška I., Bouillard P., Dispersion and pollution of the FEM solution for the helmholtz equation in one, two and three dimensions. International Journal for Numerical Methods in Engineering 1999 46 4 471 499 2-s2.0-0344549300 (Pubitemid 29487822)
    • (1999) International Journal for Numerical Methods in Engineering , vol.46 , Issue.4 , pp. 471-499
    • Deraemaeker, A.1    Babuska, I.2    Bouillard, P.3
  • 3
    • 79953076224 scopus 로고    scopus 로고
    • A mixed hybrid finite element method for the Helmholtz equation
    • 10.1080/09500340.2010.527067 MR2784456 ZBL1230.65126
    • Hannukainen A., Huber M., Schöberl J., A mixed hybrid finite element method for the Helmholtz equation. Journal of Modern Optics 2011 58 5-6 424 437 10.1080/09500340.2010.527067 MR2784456 ZBL1230.65126
    • (2011) Journal of Modern Optics , vol.58 , Issue.5-6 , pp. 424-437
    • Hannukainen, A.1    Huber, M.2    Schöberl, J.3
  • 4
    • 24944474278 scopus 로고    scopus 로고
    • Application of He's variational iteration method to Helmholtz equation
    • DOI 10.1016/j.chaos.2005.04.113, PII S096007790500473X
    • Momani S., Abuasad S., Application of He's variational iteration method to Helmholtz equation. Chaos, Solitons & Fractals 2006 27 5 1119 1123 10.1016/j.chaos.2005.04.113 MR2164845 ZBL1086.65113 (Pubitemid 41329806)
    • (2006) Chaos, Solitons and Fractals , vol.27 , Issue.5 , pp. 1119-1123
    • Momani, S.1    Abuasad, S.2
  • 5
    • 33745965279 scopus 로고    scopus 로고
    • Explicit solutions of Helmholtz equation and fifth-order KdV equation using homotopy perturbation method
    • Rafei M., Ganji D. D., Explicit solutions of Helmholtz equation and fifth-order KdV equation using homotopy perturbation method. International Journal of Nonlinear Sciences and Numerical Simulation 2006 7 3 321 328 2-s2.0-33745965279 (Pubitemid 44059427)
    • (2006) International Journal of Nonlinear Sciences and Numerical Simulation , vol.7 , Issue.3 , pp. 321-328
    • Rafei, M.1    Ganji, D.D.2
  • 6
    • 0031234450 scopus 로고    scopus 로고
    • A domain decomposition method for the Helmholtz equation and related optimal control problems
    • DOI 10.1006/jcph.1997.5742, PII S0021999197957429
    • Benamou J.-D., Desprès B., A domain decomposition method for the Helmholtz equation and related optimal control problems. Journal of Computational Physics 1997 136 1 68 82 10.1006/jcph.1997.5742 MR1468624 ZBL0884.65118 (Pubitemid 127170091)
    • (1997) Journal of Computational Physics , vol.136 , Issue.1 , pp. 68-82
    • Benamou, J.-D.1    Despres, B.2
  • 7
    • 0346669951 scopus 로고    scopus 로고
    • A fast multi-level boundary element method for the Helmholtz equation
    • DOI 10.1016/j.cma.2003.09.004
    • Grigoriev M. M., Dargush G. F., A fast multi-level boundary element method for the Helmholtz equation. Computer Methods in Applied Mechanics and Engineering 2004 193 3-5 165 203 10.1016/j.cma.2003.09.004 MR2031228 ZBL1075.76587 (Pubitemid 38086749)
    • (2004) Computer Methods in Applied Mechanics and Engineering , vol.193 , Issue.3-5 , pp. 165-203
    • Grigoriev, M.M.1    Dargush, G.F.2
  • 8
    • 0033101866 scopus 로고    scopus 로고
    • Internal field error reduction in boundary element analysis for Helmholtz equation
    • 2-s2.0-0033101866
    • Tomioka S., Nisiyama S., Itagaki M., Enoto T., Internal field error reduction in boundary element analysis for Helmholtz equation. Engineering Analysis with Boundary Elements 1999 23 3 211 222 2-s2.0-0033101866
    • (1999) Engineering Analysis with Boundary Elements , vol.23 , Issue.3 , pp. 211-222
    • Tomioka, S.1    Nisiyama, S.2    Itagaki, M.3    Enoto, T.4
  • 9
    • 1942475366 scopus 로고    scopus 로고
    • A modified Fourier-Galerkin method for the Poisson and Helmholtz equations
    • 2-s2.0-1942475366
    • Næss O. F., Eckhoff K. S., A modified Fourier-Galerkin method for the Poisson and Helmholtz equations. Journal of Scientific Computing 2002 17 1-4 529 539 2-s2.0-1942475366
    • (2002) Journal of Scientific Computing , vol.17 , Issue.1-4 , pp. 529-539
    • Næss, O.F.1    Eckhoff, K.S.2
  • 10
    • 0032066150 scopus 로고    scopus 로고
    • The Green's function for the two-dimensional Helmholtz equation in periodic domains
    • 10.1023/A:1004377501747 MR1638860 ZBL0922.76274
    • Linton C. M., The Green's function for the two-dimensional Helmholtz equation in periodic domains. Journal of Engineering Mathematics 1998 33 4 377 401 10.1023/A:1004377501747 MR1638860 ZBL0922.76274
    • (1998) Journal of Engineering Mathematics , vol.33 , Issue.4 , pp. 377-401
    • Linton, C.M.1
  • 11
    • 57249083915 scopus 로고    scopus 로고
    • Lattice sums and the two-dimensional, periodic Green's function for the Helmholtz equation
    • 10.1098/rspa.2000.0656 MR1843935 ZBL1048.78015
    • Dienstfrey A., Hang F., Huang J., Lattice sums and the two-dimensional, periodic Green's function for the Helmholtz equation. Proceedings of the Royal Society A 2001 457 2005 67 85 10.1098/rspa.2000.0656 MR1843935 ZBL1048.78015
    • (2001) Proceedings of the Royal Society A , vol.457 , Issue.2005 , pp. 67-85
    • Dienstfrey, A.1    Hang, F.2    Huang, J.3
  • 13
    • 36249022993 scopus 로고    scopus 로고
    • San Diego, Calif, USA Academic Press Mathematics in Science and Engineering MR1658022
    • Podlubny I., Fractional Differential Equations 1999 198 San Diego, Calif, USA Academic Press xxiv+340 Mathematics in Science and Engineering MR1658022
    • (1999) Fractional Differential Equations , vol.198
    • Podlubny, I.1
  • 14
    • 0004315248 scopus 로고    scopus 로고
    • New York, NY, USA Springer Institute for Nonlinear Science 10.1007/978-0-387-21746-8 MR1988873
    • West B. J., Bologna M., Grigolini P., Physics of Fractal Operators 2003 New York, NY, USA Springer x+354 Institute for Nonlinear Science 10.1007/978-0-387-21746-8 MR1988873
    • (2003) Physics of Fractal Operators
    • West, B.J.1    Bologna, M.2    Grigolini, P.3
  • 22
    • 76549127762 scopus 로고    scopus 로고
    • 2nd Berlin, Germany Springer 10.1007/978-3-642-20545-3 MR2807926
    • Das S., Functional Fractional Calculus 2011 2nd Berlin, Germany Springer xxviii+612 10.1007/978-3-642-20545-3 MR2807926
    • (2011) Functional Fractional Calculus
    • Das, S.1
  • 27
    • 2142704418 scopus 로고    scopus 로고
    • Fractional dynamics, Cantorian space-time and the gauge hierarchy problem
    • 2-s2.0-2142704418 10.1016/j.chaos.2004.02.043
    • Goldfain E., Fractional dynamics, Cantorian space-time and the gauge hierarchy problem. Chaos, Solitons & Fractals 2004 22 3 513 520 2-s2.0-2142704418 10.1016/j.chaos.2004.02.043
    • (2004) Chaos, Solitons & Fractals , vol.22 , Issue.3 , pp. 513-520
    • Goldfain, E.1
  • 28
    • 84881538901 scopus 로고    scopus 로고
    • On fractional Helmholtz equations
    • MR2761355 ZBL1223.26013
    • Samuel M. S., Thomas A., On fractional Helmholtz equations. Fractional Calculus & Applied Analysis 2010 13 3 295 308 MR2761355 ZBL1223.26013
    • (2010) Fractional Calculus & Applied Analysis , vol.13 , Issue.3 , pp. 295-308
    • Samuel, M.S.1    Thomas, A.2
  • 29
    • 84862079256 scopus 로고    scopus 로고
    • Application of He's homotopy perturbation method for multi-dimensional fractional Helmholtz equation
    • 10.1108/09615531211215738 MR2984748
    • Gupta P. K., Yildirim A., Rai K. N., Application of He's homotopy perturbation method for multi-dimensional fractional Helmholtz equation. International Journal of Numerical Methods for Heat & Fluid Flow 2012 22 3-4 424 435 10.1108/09615531211215738 MR2984748
    • (2012) International Journal of Numerical Methods for Heat & Fluid Flow , vol.22 , Issue.3-4 , pp. 424-435
    • Gupta, P.K.1    Yildirim, A.2    Rai, K.N.3
  • 30
    • 0001707390 scopus 로고    scopus 로고
    • Local fractional Fokker-Planck equation
    • Kolwankar K. M., Gangal A. D., Local fractional Fokker-Planck equation. Physical Review Letters 1998 80 2 214 217 10.1103/PhysRevLett.80.214 MR1604435 ZBL0945.82005 (Pubitemid 128621921)
    • (1998) Physical Review Letters , vol.80 , Issue.2 , pp. 214-217
    • Kolwankar, K.M.1    Gangal, A.D.2
  • 31
    • 0042121430 scopus 로고    scopus 로고
    • On the mechanics of quasi-brittle materials with a fractal microstructure
    • DOI 10.1016/S0013-7944(02)00220-5
    • Carpinteri A., Chiaia B., Cornetti P., On the mechanics of quasi-brittle materials with a fractal microstructure. Engineering Fracture Mechanics 2003 70 16 2321 2349 2-s2.0-0042121430 10.1016/S0013-7944(02)00220-5 (Pubitemid 36941621)
    • (2003) Engineering Fracture Mechanics , vol.70 , Issue.16 , pp. 2321-2349
    • Carpinteri, A.1    Chiaia, B.2    Cornetti, P.3
  • 32
    • 0035891478 scopus 로고    scopus 로고
    • About non-differentiable functions
    • DOI 10.1006/jmaa.2001.7656
    • Ben Adda F., Cresson J., About non-differentiable functions. Journal of Mathematical Analysis and Applications 2001 263 2 721 737 10.1006/jmaa.2001.7656 MR1866075 ZBL0995.26006 (Pubitemid 33132693)
    • (2001) Journal of Mathematical Analysis and Applications , vol.263 , Issue.2 , pp. 721-737
    • Ben Adda, F.1    Cresson, J.2
  • 33
    • 0036600978 scopus 로고    scopus 로고
    • On calculus of local fractional derivatives
    • 10.1016/S0022-247X(02)00048-3 MR1911751 ZBL1005.26002
    • Babakhani A., Daftardar-Gejji V., On calculus of local fractional derivatives. Journal of Mathematical Analysis and Applications 2002 270 1 66 79 10.1016/S0022-247X(02)00048-3 MR1911751 ZBL1005.26002
    • (2002) Journal of Mathematical Analysis and Applications , vol.270 , Issue.1 , pp. 66-79
    • Babakhani, A.1    Daftardar-Gejji, V.2
  • 34
    • 70350325151 scopus 로고    scopus 로고
    • On the local fractional derivative
    • 10.1016/j.jmaa.2009.08.014 MR2557664 ZBL1196.26011
    • Chen Y., Yan Y., Zhang K., On the local fractional derivative. Journal of Mathematical Analysis and Applications 2010 362 1 17 33 10.1016/j.jmaa.2009.08. 014 MR2557664 ZBL1196.26011
    • (2010) Journal of Mathematical Analysis and Applications , vol.362 , Issue.1 , pp. 17-33
    • Chen, Y.1    Yan, Y.2    Zhang, K.3
  • 35
    • 76449111034 scopus 로고    scopus 로고
    • Anomalous diffusion modeling by fractal and fractional derivatives
    • 10.1016/j.camwa.2009.08.020 MR2595948 ZBL1189.35355
    • Chen W., Sun H., Zhang X., Korošak D., Anomalous diffusion modeling by fractal and fractional derivatives. Computers & Mathematics with Applications 2010 59 5 1754 1758 10.1016/j.camwa.2009.08.020 MR2595948 ZBL1189.35355
    • (2010) Computers & Mathematics with Applications , vol.59 , Issue.5 , pp. 1754-1758
    • Chen, W.1    Sun, H.2    Zhang, X.3    Korošak, D.4
  • 39
    • 84881521586 scopus 로고    scopus 로고
    • Helmholtz and diffusion equations associated with local fractional derivative operators involving the Cantorian and Cantor-type cylindrical coordinates
    • 10.1155/2013/754248 754248 MR3079019
    • Hao Y.-J., Srivastava H. M., Jafari H., Yang X.-J., Helmholtz and diffusion equations associated with local fractional derivative operators involving the Cantorian and Cantor-type cylindrical coordinates. Advances in Mathematical Physics 2013 2013 5 10.1155/2013/754248 754248 MR3079019
    • (2013) Advances in Mathematical Physics , vol.2013 , pp. 5
    • Hao, Y.-J.1    Srivastava, H.M.2    Jafari, H.3    Yang, X.-J.4
  • 40
    • 84879302696 scopus 로고    scopus 로고
    • Local fractional series expansion method for solving wave and diffusion equations on Cantor sets
    • 10.1155/2013/351057 351057 MR3064518
    • Yang A.-M., Yang X.-J., Li Z.-B., Local fractional series expansion method for solving wave and diffusion equations on Cantor sets. Abstract and Applied Analysis 2013 2013 5 10.1155/2013/351057 351057 MR3064518
    • (2013) Abstract and Applied Analysis , vol.2013 , pp. 5
    • Yang, A.-M.1    Yang, X.-J.2    Li, Z.-B.3
  • 41
    • 84879324154 scopus 로고    scopus 로고
    • Fractal heat conduction problem solved by local fractional variation iteration method
    • Yang X.-J., Baleanu D., Fractal heat conduction problem solved by local fractional variation iteration method. Thermal Science 2013 17 2 625 628
    • (2013) Thermal Science , vol.17 , Issue.2 , pp. 625-628
    • Yang, X.-J.1    Baleanu, D.2
  • 42
    • 84879310679 scopus 로고    scopus 로고
    • Damped wave equation and dissipative wave equation in fractal strings within the local fractional variational iteration method
    • 10.1186/1687-1812-2013-89 MR3053815 ARTICLE 89
    • Su W.-H., Baleanu D., Yang X.-J., Jafari H., Damped wave equation and dissipative wave equation in fractal strings within the local fractional variational iteration method. Fixed Point Theory and Applications 2013 2013 1, article 89 1 11 10.1186/1687-1812-2013-89 MR3053815
    • (2013) Fixed Point Theory and Applications , vol.2013 , Issue.1 , pp. 1-11
    • Su, W.-H.1    Baleanu, D.2    Yang, X.-J.3    Jafari, H.4
  • 43
    • 84877292735 scopus 로고    scopus 로고
    • A local fractional variational iteration method for Laplace equation within local fractional operators
    • 10.1155/2013/202650 202650 MR3045074 ZBL06209209
    • Yang Y.-J., Baleanu D., Yang X.-J., A local fractional variational iteration method for Laplace equation within local fractional operators. Abstract and Applied Analysis 2013 2013 6 10.1155/2013/202650 202650 MR3045074 ZBL06209209
    • (2013) Abstract and Applied Analysis , vol.2013 , pp. 6
    • Yang, Y.-J.1    Baleanu, D.2    Yang, X.-J.3
  • 44
    • 84884837318 scopus 로고    scopus 로고
    • Local fractional variational iteration method for fractal heat transfer in silk cocoon hierarchy
    • He J.-H., Local fractional variational iteration method for fractal heat transfer in silk cocoon hierarchy. Nonlinear Science Letters A 2013 4 1 15 20
    • (2013) Nonlinear Science Letters A , vol.4 , Issue.1 , pp. 15-20
    • He, J.-H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.