메뉴 건너뛰기




Volumn 245-246, Issue , 2012, Pages 132-143

Analyzing two-dimensional sine-Gordon equation with the mesh-free reproducing kernel particle Ritz method

Author keywords

Mesh free kp Ritz method; Meshless method; Sine Gordon (SG) equation; Soliton

Indexed keywords

2-D DISPLACEMENT; ENERGY EXPRESSION; MESH-LESS METHODS; MESHFREE; REPRODUCING KERNEL; RITZ METHODS; SINE-GORDON (SG) EQUATION; SYSTEM OF DISCRETE EQUATION;

EID: 84864797575     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2012.07.010     Document Type: Article
Times cited : (45)

References (44)
  • 3
    • 40749131187 scopus 로고    scopus 로고
    • A numerical method for one-dimensional nonlinear sine-Gordon equation using collocation and radial basis functions
    • Dehghan M., Shokri A. A numerical method for one-dimensional nonlinear sine-Gordon equation using collocation and radial basis functions. Numer. Methods Partial Differ. Equat. 2008, 32:687-698.
    • (2008) Numer. Methods Partial Differ. Equat. , vol.32 , pp. 687-698
    • Dehghan, M.1    Shokri, A.2
  • 4
    • 66049106086 scopus 로고    scopus 로고
    • Fourth-order compact scheme for the one-dimensional sine-Gordon equation
    • Cui M. Fourth-order compact scheme for the one-dimensional sine-Gordon equation. Numer. Methods Partial Differ. Equat. 2009, 25:685-711.
    • (2009) Numer. Methods Partial Differ. Equat. , vol.25 , pp. 685-711
    • Cui, M.1
  • 6
    • 0035841403 scopus 로고    scopus 로고
    • The sine-Gordon equation in the finite line
    • Ramos J.I. The sine-Gordon equation in the finite line. Appl. Math. Comput. 2001, 124:45-93.
    • (2001) Appl. Math. Comput. , vol.124 , pp. 45-93
    • Ramos, J.I.1
  • 7
    • 0023306712 scopus 로고
    • An engineer's guide to soliton phenomena: application of the finite element method
    • Argyris J., Haase M. An engineer's guide to soliton phenomena: application of the finite element method. Comput. Methods Appl. Mech. Engrg. 1987, 61:71-122.
    • (1987) Comput. Methods Appl. Mech. Engrg. , vol.61 , pp. 71-122
    • Argyris, J.1    Haase, M.2
  • 9
    • 0002025756 scopus 로고
    • Two energy conserving numerical schemes for the sine-Gordon equation
    • Fei Z., Vázquez L. Two energy conserving numerical schemes for the sine-Gordon equation. Appl. Math. Comput. 1991, 45:17-30.
    • (1991) Appl. Math. Comput. , vol.45 , pp. 17-30
    • Fei, Z.1    Vázquez, L.2
  • 10
    • 27844591478 scopus 로고    scopus 로고
    • Energy conserving difference scheme for initial-boundary value problem of the sine-Gordon equation
    • Zhang L. Energy conserving difference scheme for initial-boundary value problem of the sine-Gordon equation. J. Univ. Petrol. China 1999, 23:100-103.
    • (1999) J. Univ. Petrol. China , vol.23 , pp. 100-103
    • Zhang, L.1
  • 11
    • 74249104801 scopus 로고
    • A conserving nine points finite difference scheme for the sine-Gordon equation
    • Zhang L., Chang Q. A conserving nine points finite difference scheme for the sine-Gordon equation. Math. Appl. 1992, 12:30-35.
    • (1992) Math. Appl. , vol.12 , pp. 30-35
    • Zhang, L.1    Chang, Q.2
  • 12
    • 35248814929 scopus 로고    scopus 로고
    • Multi-Symplectic Spectral Methods for the Sine-Gordon Equation
    • Springer-Verlag, Berlin-Heidelberg
    • Islas A.L., Schober C.M. Multi-Symplectic Spectral Methods for the Sine-Gordon Equation. Lecture Notes in Comput. Sci. 2003, vol. 2658. Springer-Verlag, Berlin-Heidelberg.
    • (2003) Lecture Notes in Comput. Sci. , vol.2658
    • Islas, A.L.1    Schober, C.M.2
  • 13
    • 84866981488 scopus 로고    scopus 로고
    • Symplectic computation of solitary waves for general sine-Gordon equations
    • Lu X. Symplectic computation of solitary waves for general sine-Gordon equations. Math. Comput. Simulation 1999, 50:225-263.
    • (1999) Math. Comput. Simulation , vol.50 , pp. 225-263
    • Lu, X.1
  • 14
    • 0037507444 scopus 로고    scopus 로고
    • A numerical solution of the sine-Gordon equation using the modified decomposition method
    • Dǒgan Kaya A numerical solution of the sine-Gordon equation using the modified decomposition method. Appl. Math. Comput. 2003, 143:309-317.
    • (2003) Appl. Math. Comput. , vol.143 , pp. 309-317
    • Dǒgan, K.1
  • 15
    • 77951141716 scopus 로고    scopus 로고
    • Generalized Jacobi rational spectral method and its applications
    • Guo B.Y., Yi Y.G. Generalized Jacobi rational spectral method and its applications. J. Sci. Comput. 2010, 43:201-238.
    • (2010) J. Sci. Comput. , vol.43 , pp. 201-238
    • Guo, B.Y.1    Yi, Y.G.2
  • 16
    • 63449096068 scopus 로고    scopus 로고
    • Application of homotopy-perturbation method to Klein-Gordon and sine-Gordon equations
    • Chowdhury M.S.H., Hashim I. Application of homotopy-perturbation method to Klein-Gordon and sine-Gordon equations. Chaos Solitons Fract. 2009, 39:1928-1935.
    • (2009) Chaos Solitons Fract. , vol.39 , pp. 1928-1935
    • Chowdhury, M.S.H.1    Hashim, I.2
  • 17
    • 56249086875 scopus 로고    scopus 로고
    • The boundary integral equation approach for numerical solution of the one-dimensional sine-Gordon equation
    • Dehghan M., Mirzaei D. The boundary integral equation approach for numerical solution of the one-dimensional sine-Gordon equation. Numer. Methods Partial Differ. Equat. 2008, 24:1405-1415.
    • (2008) Numer. Methods Partial Differ. Equat. , vol.24 , pp. 1405-1415
    • Dehghan, M.1    Mirzaei, D.2
  • 19
    • 0041185368 scopus 로고
    • A review of the decomposition method in applied mathematics
    • Adomian G. A review of the decomposition method in applied mathematics. J. Math. Anal. Appl. 1988, 135:501-544.
    • (1988) J. Math. Anal. Appl. , vol.135 , pp. 501-544
    • Adomian, G.1
  • 20
    • 56149124076 scopus 로고    scopus 로고
    • A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions
    • Dehghan M., Shokri A. A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions. Mathematics and Computers in Simulation 2008, 79:700-715.
    • (2008) Mathematics and Computers in Simulation , vol.79 , pp. 700-715
    • Dehghan, M.1    Shokri, A.2
  • 21
    • 73449115631 scopus 로고    scopus 로고
    • Meshless local Petrov-Galerkin (MLPG) approximation to the two-dimensional sine-Gordon equation
    • Mirzaei D., Dehghan M. Meshless local Petrov-Galerkin (MLPG) approximation to the two-dimensional sine-Gordon equation. J. Comput. Appl. Math. 2010, 233:2737-2754.
    • (2010) J. Comput. Appl. Math. , vol.233 , pp. 2737-2754
    • Mirzaei, D.1    Dehghan, M.2
  • 22
    • 78149416097 scopus 로고    scopus 로고
    • Multilevel augmentation methods for solving sine-Gordon equation
    • Chen J., Cheng Z.G., Cheng S.R. Multilevel augmentation methods for solving sine-Gordon equation. J. Math. Anal. Appl. 2011, 375:706-724.
    • (2011) J. Math. Anal. Appl. , vol.375 , pp. 706-724
    • Chen, J.1    Cheng, Z.G.2    Cheng, S.R.3
  • 23
    • 0347945239 scopus 로고    scopus 로고
    • Discrete singular convolution for the sine-Gordon equation
    • Wei G.W. Discrete singular convolution for the sine-Gordon equation. Physica D 2000, 137:247-259.
    • (2000) Physica D , vol.137 , pp. 247-259
    • Wei, G.W.1
  • 24
    • 26444583020 scopus 로고    scopus 로고
    • Discrete singular convolution for the solution of the Fokker-Planck equation
    • Wei G.W. Discrete singular convolution for the solution of the Fokker-Planck equation. J. Chem. Phys. 1999, 110:8930-8942.
    • (1999) J. Chem. Phys. , vol.110 , pp. 8930-8942
    • Wei, G.W.1
  • 25
    • 0035850205 scopus 로고    scopus 로고
    • Vibration analysis by discrete singular convolution
    • Wei G.W. Vibration analysis by discrete singular convolution. J. Sound Vib. 2001, 244:535-553.
    • (2001) J. Sound Vib. , vol.244 , pp. 535-553
    • Wei, G.W.1
  • 26
    • 0035808191 scopus 로고    scopus 로고
    • A new algorithm for solving some mechanical problems
    • Wei G.W. A new algorithm for solving some mechanical problems. Comput. Methods Appl. Mech. Engrg. 2001, 190:2017-2030.
    • (2001) Comput. Methods Appl. Mech. Engrg. , vol.190 , pp. 2017-2030
    • Wei, G.W.1
  • 27
    • 0035427408 scopus 로고    scopus 로고
    • The determination of natural frequencies of rectangular plates with mixed boundary conditions by discrete singular convolution
    • Wei G.W., Zhao Y.B., Xiang Y. The determination of natural frequencies of rectangular plates with mixed boundary conditions by discrete singular convolution. Int. J. Mech. Sci. 2001, 43:1731-1746.
    • (2001) Int. J. Mech. Sci. , vol.43 , pp. 1731-1746
    • Wei, G.W.1    Zhao, Y.B.2    Xiang, Y.3
  • 28
    • 0035451995 scopus 로고    scopus 로고
    • Discrete singular convolution for beam analysis
    • Wei G.W. Discrete singular convolution for beam analysis. Engrg. Struct. 2001, 23:1045-1053.
    • (2001) Engrg. Struct. , vol.23 , pp. 1045-1053
    • Wei, G.W.1
  • 29
    • 75749106945 scopus 로고    scopus 로고
    • Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM)
    • Dehghan Mehdi, Ghesmati Arezou Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM). Comput. Phys. Commun. 2010, 181:772-786.
    • (2010) Comput. Phys. Commun. , vol.181 , pp. 772-786
    • Dehghan, M.1    Ghesmati, A.2
  • 30
    • 74149087057 scopus 로고    scopus 로고
    • High-order solution of one-dimensional sine-Gordon equation using compact finite difference and DIRKN methods
    • Mohebbi Akbar, Dehghan Mehdi High-order solution of one-dimensional sine-Gordon equation using compact finite difference and DIRKN methods. Math. Comput. Model. 2010, 51:537-549.
    • (2010) Math. Comput. Model. , vol.51 , pp. 537-549
    • Mohebbi, A.1    Dehghan, M.2
  • 31
    • 56249085908 scopus 로고    scopus 로고
    • Boundary element solution of the two-dimensional sine-Gordon equation using continuous linear elements
    • Mirzaei Davoud, Dehghan Mehdi Boundary element solution of the two-dimensional sine-Gordon equation using continuous linear elements. Engrg. Anal. Boundary Elem. 2009, 33:12-24.
    • (2009) Engrg. Anal. Boundary Elem. , vol.33 , pp. 12-24
    • Mirzaei, D.1    Dehghan, M.2
  • 32
    • 70249128335 scopus 로고    scopus 로고
    • Implementation of meshless LBIE method to the 2D non-linear SG problem
    • Mirzaei Davoud, Dehghan Mehdi Implementation of meshless LBIE method to the 2D non-linear SG problem. Int. J. Numer. Methods Engrg. 2009, 79:1662-1682.
    • (2009) Int. J. Numer. Methods Engrg. , vol.79 , pp. 1662-1682
    • Mirzaei, D.1    Dehghan, M.2
  • 33
    • 36048991845 scopus 로고    scopus 로고
    • The dual reciprocity boundary element method (DRBEM) for two-dimensional sine-Gordon equation
    • Dehghan Mehdi, Mirzaei Davoud The dual reciprocity boundary element method (DRBEM) for two-dimensional sine-Gordon equation. Comput. Methods Appl. Mech. Engrg. 2008, 197:476-486.
    • (2008) Comput. Methods Appl. Mech. Engrg. , vol.197 , pp. 476-486
    • Dehghan, M.1    Mirzaei, D.2
  • 34
    • 0343262489 scopus 로고
    • über eine neue methode zur lösung gewisser variationsprobleme der mathematischen physic
    • Ritz W. über eine neue methode zur lösung gewisser variationsprobleme der mathematischen physic. J. Reine Angew. Math. 1909, 135:1-61.
    • (1909) J. Reine Angew. Math. , vol.135 , pp. 1-61
    • Ritz, W.1
  • 35
    • 0003951930 scopus 로고
    • Macmillan, New York, (reprinted by Dover Publications in 1945)
    • Rayleigh J.W. Theory of Sound 1877, vol. 1. Macmillan, New York, (reprinted by Dover Publications in 1945).
    • (1877) Theory of Sound , vol.1
    • Rayleigh, J.W.1
  • 37
  • 39
    • 0035415918 scopus 로고    scopus 로고
    • Free vibrations of rectangular unsymmetrically laminated composite plates with internal line supports
    • Cheung Y.K., Zhou D. Free vibrations of rectangular unsymmetrically laminated composite plates with internal line supports. Comput. Struct. 2001, 79:1923-1932.
    • (2001) Comput. Struct. , vol.79 , pp. 1923-1932
    • Cheung, Y.K.1    Zhou, D.2
  • 40
    • 0037084909 scopus 로고    scopus 로고
    • Three-dimensional vibration analysis of cantilevered and completely free isosceles triangular plates
    • Cheung Y.K., Zhou D. Three-dimensional vibration analysis of cantilevered and completely free isosceles triangular plates. Int. J. Solids Struct. 2002, 39:673-687.
    • (2002) Int. J. Solids Struct. , vol.39 , pp. 673-687
    • Cheung, Y.K.1    Zhou, D.2
  • 41
    • 33846555143 scopus 로고    scopus 로고
    • Free vibration analysis of discretely stiffened skew plates
    • Zeng H., Bert C.W. Free vibration analysis of discretely stiffened skew plates. Int. J. Stability Dynam. 2001, 1:125-144.
    • (2001) Int. J. Stability Dynam. , vol.1 , pp. 125-144
    • Zeng, H.1    Bert, C.W.2
  • 42
    • 0036569003 scopus 로고    scopus 로고
    • A non-discrete approach for analysis of plates with multiple subdomains
    • Su G.H., Xiang Y. A non-discrete approach for analysis of plates with multiple subdomains. Engrg. Struct. 2002, 24:563-575.
    • (2002) Engrg. Struct. , vol.24 , pp. 563-575
    • Su, G.H.1    Xiang, Y.2
  • 43
    • 0028769407 scopus 로고
    • A pb-2 Ritz formulation for flexural vibration of shallow cylindrical shells of rectangular platform
    • Lim C.W., Liew K.M. A pb-2 Ritz formulation for flexural vibration of shallow cylindrical shells of rectangular platform. J. Sound Vib. 1994, 173:343-375.
    • (1994) J. Sound Vib. , vol.173 , pp. 343-375
    • Lim, C.W.1    Liew, K.M.2
  • 44
    • 0035501679 scopus 로고    scopus 로고
    • Three-dimensional free vibration analysis of perforated super elliptical plates via the p-Ritz method
    • Liew K.M., Feng Z.C. Three-dimensional free vibration analysis of perforated super elliptical plates via the p-Ritz method. Int. J. Mech. Sci. 2001, 43:2613-2630.
    • (2001) Int. J. Mech. Sci. , vol.43 , pp. 2613-2630
    • Liew, K.M.1    Feng, Z.C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.