메뉴 건너뛰기




Volumn 181, Issue 4, 2010, Pages 772-786

Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM)

Author keywords

Conservation of energy; Line and ring solitons; Local radial point interpolation method (LRPIM); Meshless weak form; Sine Gordon equation; Soliton; Truly meshless method

Indexed keywords

CONSERVATION OF ENERGY; LOCAL RADIAL POINT INTERPOLATION METHODS; MESHLESS; RING SOLITONS; SINE-GORDON EQUATION; TRULY MESHLESS METHODS; WEAK FORM;

EID: 75749106945     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cpc.2009.12.010     Document Type: Article
Times cited : (186)

References (63)
  • 1
    • 0026124767 scopus 로고
    • Finite element approximation to two-dimensional sine-Gordon solitons
    • Argyris J., Haase M., and Heinrich J.C. Finite element approximation to two-dimensional sine-Gordon solitons. Comput. Meth. Appl. Mech. Eng. 86 (1991) 1-26
    • (1991) Comput. Meth. Appl. Mech. Eng. , vol.86 , pp. 1-26
    • Argyris, J.1    Haase, M.2    Heinrich, J.C.3
  • 2
    • 0032136132 scopus 로고    scopus 로고
    • A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics
    • Atluri S.N., and Zhu T. A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput. Mech. 22 (1998) 117-127
    • (1998) Comput. Mech. , vol.22 , pp. 117-127
    • Atluri, S.N.1    Zhu, T.2
  • 3
    • 0001022815 scopus 로고    scopus 로고
    • A new meshless local Petrov-Galerkin (MLPG) approach to nonlinear problems in computer modeling and simulation
    • Atluri S.N., and Zhu T. A new meshless local Petrov-Galerkin (MLPG) approach to nonlinear problems in computer modeling and simulation. Comput. Model. Simul. Eng. 3 3 (1998) 187-196
    • (1998) Comput. Model. Simul. Eng. , vol.3 , Issue.3 , pp. 187-196
    • Atluri, S.N.1    Zhu, T.2
  • 5
    • 0033872785 scopus 로고    scopus 로고
    • The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics
    • Atluri S.N., and Zhu T. The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics. Comput. Mech. 25 (2000) 169-179
    • (2000) Comput. Mech. , vol.25 , pp. 169-179
    • Atluri, S.N.1    Zhu, T.2
  • 7
    • 0029378909 scopus 로고
    • Element free Galerkin methods for static and dynamic fracture
    • Belytschko T., Lu Y.Y., and Gu L. Element free Galerkin methods for static and dynamic fracture. Int. J. Solids Struct. 32 (1995) 2547-2570
    • (1995) Int. J. Solids Struct. , vol.32 , pp. 2547-2570
    • Belytschko, T.1    Lu, Y.Y.2    Gu, L.3
  • 8
    • 0023166078 scopus 로고
    • Applications of smoothed particle hydrodynamics (SPH) to astrophysical problems
    • Benz W. Applications of smoothed particle hydrodynamics (SPH) to astrophysical problems. Comput. Phys. Comm. 48 (1988) 97-105
    • (1988) Comput. Phys. Comm. , vol.48 , pp. 97-105
    • Benz, W.1
  • 9
    • 50449092707 scopus 로고    scopus 로고
    • An improved numerical scheme for the sine-Gordon equation in 2 + 1 dimensions
    • Bratsos A.G. An improved numerical scheme for the sine-Gordon equation in 2 + 1 dimensions. Int. J. Numer. Meth. Eng. 75 (2008) 787-799
    • (2008) Int. J. Numer. Meth. Eng. , vol.75 , pp. 787-799
    • Bratsos, A.G.1
  • 10
    • 33847382284 scopus 로고    scopus 로고
    • An explicit numerical scheme for the sine-Gordon equation in 2 + 1 dimensions
    • Bratsos A.G. An explicit numerical scheme for the sine-Gordon equation in 2 + 1 dimensions. Appl. Numer. Anal. Comput. Math. 2 (2005) 189-211
    • (2005) Appl. Numer. Anal. Comput. Math. , vol.2 , pp. 189-211
    • Bratsos, A.G.1
  • 11
    • 35748982165 scopus 로고    scopus 로고
    • A third order numerical scheme for the two-dimensional, sine-Gordon equation
    • Bratsos A.G. A third order numerical scheme for the two-dimensional, sine-Gordon equation. Math. Comput. Simul. 76 (2007) 271-282
    • (2007) Math. Comput. Simul. , vol.76 , pp. 271-282
    • Bratsos, A.G.1
  • 12
    • 33847407493 scopus 로고    scopus 로고
    • A modified predictor-corrector scheme for the two-dimensional sine-Gordon equation
    • Bratsos A.G. A modified predictor-corrector scheme for the two-dimensional sine-Gordon equation. Numer. Algor. 43 (2006) 295-308
    • (2006) Numer. Algor. , vol.43 , pp. 295-308
    • Bratsos, A.G.1
  • 13
    • 34249277434 scopus 로고    scopus 로고
    • The solution of the two-dimensional sine-Gordon equation using the method of lines
    • Bratsos A.G. The solution of the two-dimensional sine-Gordon equation using the method of lines. J. Comput. Appl. Math. 206 (2007) 251-277
    • (2007) J. Comput. Appl. Math. , vol.206 , pp. 251-277
    • Bratsos, A.G.1
  • 14
    • 0001329612 scopus 로고
    • Numerical solution of 2 + 1 dimensional sine-Gordon solitons
    • Christiansen P.L., and Lomdahl P.S. Numerical solution of 2 + 1 dimensional sine-Gordon solitons. Physica D 2 (1981) 482-494
    • (1981) Physica D , vol.2 , pp. 482-494
    • Christiansen, P.L.1    Lomdahl, P.S.2
  • 15
    • 0032436773 scopus 로고    scopus 로고
    • Modeling conned multi-material heat and mass flows using SPH
    • Clear P.W. Modeling conned multi-material heat and mass flows using SPH. Appl. Math. Model. 22 (1998) 981-993
    • (1998) Appl. Math. Model. , vol.22 , pp. 981-993
    • Clear, P.W.1
  • 17
    • 36048991845 scopus 로고    scopus 로고
    • The dual reciprocity boundary element method (DRBEM) for two-dimensional sine-Gordon equation
    • Dehghan M., and Mirzaei D. The dual reciprocity boundary element method (DRBEM) for two-dimensional sine-Gordon equation. Comput. Meth. Appl. Mech. Eng. 197 (2008) 476-486
    • (2008) Comput. Meth. Appl. Mech. Eng. , vol.197 , pp. 476-486
    • Dehghan, M.1    Mirzaei, D.2
  • 18
    • 56149124076 scopus 로고    scopus 로고
    • A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions
    • Dehghan M., and Shokri A. A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions. Math. Comput. Simul. 79 (2008) 700-715
    • (2008) Math. Comput. Simul. , vol.79 , pp. 700-715
    • Dehghan, M.1    Shokri, A.2
  • 19
    • 47049117992 scopus 로고    scopus 로고
    • The meshless local Petrov-Galerkin (MLPG) method for the generalized two-dimensional non-linear Schrödinger equation
    • Dehghan M., and Mirzaei D. The meshless local Petrov-Galerkin (MLPG) method for the generalized two-dimensional non-linear Schrödinger equation. Eng. Anal. Bound. Elem. 32 (2008) 747-756
    • (2008) Eng. Anal. Bound. Elem. , vol.32 , pp. 747-756
    • Dehghan, M.1    Mirzaei, D.2
  • 20
    • 61549088742 scopus 로고    scopus 로고
    • Meshless local Petrov-Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity
    • Dehghan M., and Mirzaei D. Meshless local Petrov-Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity. Appl. Numer. Math. 59 (2009) 1043-1058
    • (2009) Appl. Numer. Math. , vol.59 , pp. 1043-1058
    • Dehghan, M.1    Mirzaei, D.2
  • 21
    • 32644435892 scopus 로고    scopus 로고
    • Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices
    • Dehghan M. Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices. Math. Comput. Simul. 71 (2006) 16-30
    • (2006) Math. Comput. Simul. , vol.71 , pp. 16-30
    • Dehghan, M.1
  • 22
    • 0000882148 scopus 로고    scopus 로고
    • The method of finite spheres
    • De S., and Bathe K.J. The method of finite spheres. Comput. Mech. 25 (2000) 329-345
    • (2000) Comput. Mech. , vol.25 , pp. 329-345
    • De, S.1    Bathe, K.J.2
  • 23
    • 0029332275 scopus 로고
    • Numerical solutions of a damped sine-Gordon equation in two space variables
    • Djidjeli K., Price W.G., and Twizell E.H. Numerical solutions of a damped sine-Gordon equation in two space variables. J. Eng. Math. 29 (1995) 347-369
    • (1995) J. Eng. Math. , vol.29 , pp. 347-369
    • Djidjeli, K.1    Price, W.G.2    Twizell, E.H.3
  • 24
    • 0002245065 scopus 로고    scopus 로고
    • Solving partial differential equations by collocation using radial basis functions
    • Franke C., and Schaback R. Solving partial differential equations by collocation using radial basis functions. Appl. Math. Comput. 93 (1997) 73-82
    • (1997) Appl. Math. Comput. , vol.93 , pp. 73-82
    • Franke, C.1    Schaback, R.2
  • 25
    • 0035271335 scopus 로고    scopus 로고
    • A meshless local Petrov-Galerkin (MLPG) method for free and forced vibration analyses for solids
    • Gu Y.T., and Liu G.R. A meshless local Petrov-Galerkin (MLPG) method for free and forced vibration analyses for solids. Comput. Mech. 27 (2001) 188-198
    • (2001) Comput. Mech. , vol.27 , pp. 188-198
    • Gu, Y.T.1    Liu, G.R.2
  • 26
    • 0035261976 scopus 로고    scopus 로고
    • A boundary point interpolation method for stress analysis of solids
    • Gu Y.T., and Liu G.R. A boundary point interpolation method for stress analysis of solids. Comput. Mech. 28 (2002) 47-54
    • (2002) Comput. Mech. , vol.28 , pp. 47-54
    • Gu, Y.T.1    Liu, G.R.2
  • 27
    • 0037407334 scopus 로고    scopus 로고
    • A boundary radial point interpolation method (BRPIM) for 2-D structural analyses
    • Gu Y.T., and Liu G.R. A boundary radial point interpolation method (BRPIM) for 2-D structural analyses. Struct. Eng. Mech. 15 (2003) 535-550
    • (2003) Struct. Eng. Mech. , vol.15 , pp. 535-550
    • Gu, Y.T.1    Liu, G.R.2
  • 28
    • 0035800453 scopus 로고    scopus 로고
    • A local point interpolation method for static and dynamic analysis of thin beams
    • Gu Y.T., and Liu G.R. A local point interpolation method for static and dynamic analysis of thin beams. Comput. Meth. Appl. Mech. Eng. 190 (2001) 5515-5528
    • (2001) Comput. Meth. Appl. Mech. Eng. , vol.190 , pp. 5515-5528
    • Gu, Y.T.1    Liu, G.R.2
  • 30
    • 0036643088 scopus 로고    scopus 로고
    • Soliton solution of some nonlinear partial differential equations and its application in fluid mechanics
    • Helal M.A. Soliton solution of some nonlinear partial differential equations and its application in fluid mechanics. Chaos Solitons Fractals 13 (2002) 1917-1929
    • (2002) Chaos Solitons Fractals , vol.13 , pp. 1917-1929
    • Helal, M.A.1
  • 31
    • 33646136226 scopus 로고    scopus 로고
    • A modified meshless local Petrov-Galerkin method to elasticity problems in computer modeling and simulation
    • Hu D.A., Long S.Y., Liu K.Y., and Li G.Y. A modified meshless local Petrov-Galerkin method to elasticity problems in computer modeling and simulation. Eng. Anal. Bound. Elem. 30 (2006) 399-404
    • (2006) Eng. Anal. Bound. Elem. , vol.30 , pp. 399-404
    • Hu, D.A.1    Long, S.Y.2    Liu, K.Y.3    Li, G.Y.4
  • 32
    • 0025229330 scopus 로고
    • Multiquadrics-a scattered data approximation scheme with applications to computational fluid dynamics
    • Kansa E.J. Multiquadrics-a scattered data approximation scheme with applications to computational fluid dynamics. Comput. Math. Appl. 19 8/9 (1990) 127-145
    • (1990) Comput. Math. Appl. , vol.19 , Issue.8-9 , pp. 127-145
    • Kansa, E.J.1
  • 35
    • 0036915246 scopus 로고    scopus 로고
    • Point interpolation method based on local residual formulation using radial basis functions
    • Liu G.R., Yan L., Wang J.G., and Gu Y.T. Point interpolation method based on local residual formulation using radial basis functions. Struct. Eng. Mech. 14 (2002) 713-732
    • (2002) Struct. Eng. Mech. , vol.14 , pp. 713-732
    • Liu, G.R.1    Yan, L.2    Wang, J.G.3    Gu, Y.T.4
  • 36
    • 0035817769 scopus 로고    scopus 로고
    • A local radial point interpolation method (LR-PIM) for free vibration analyses of 2-D solids
    • Liu G.R., and Gu Y.T. A local radial point interpolation method (LR-PIM) for free vibration analyses of 2-D solids. J. Sound Vib. 246 1 (2001) 29-46
    • (2001) J. Sound Vib. , vol.246 , Issue.1 , pp. 29-46
    • Liu, G.R.1    Gu, Y.T.2
  • 37
    • 29144534039 scopus 로고    scopus 로고
    • A simple and less-costly meshless local Petrov-Galerkin (MLPG) method for the dynamic fracture problem
    • Liu K.Y., Long S.Y., and Li G.Y. A simple and less-costly meshless local Petrov-Galerkin (MLPG) method for the dynamic fracture problem. Eng. Anal. Bound. Elem. 30 (2006) 72-76
    • (2006) Eng. Anal. Bound. Elem. , vol.30 , pp. 72-76
    • Liu, K.Y.1    Long, S.Y.2    Li, G.Y.3
  • 38
    • 0035112642 scopus 로고    scopus 로고
    • A point interpolation method for two-dimensional solids
    • Liu G.R., and Gu Y.T. A point interpolation method for two-dimensional solids. Int. J. Numer. Meth. Eng. 50 (2001) 937-951
    • (2001) Int. J. Numer. Meth. Eng. , vol.50 , pp. 937-951
    • Liu, G.R.1    Gu, Y.T.2
  • 40
    • 0037981463 scopus 로고    scopus 로고
    • A matrix triangularization algorithm for the polynomial point interpolation method
    • Liu G.R., and Gu Y.T. A matrix triangularization algorithm for the polynomial point interpolation method. Comput. Meth. Appl. Mech. Eng. 192 (2003) 2269-2295
    • (2003) Comput. Meth. Appl. Mech. Eng. , vol.192 , pp. 2269-2295
    • Liu, G.R.1    Gu, Y.T.2
  • 41
    • 0030380578 scopus 로고    scopus 로고
    • The partition of unity finite element method: Basic theory and applications
    • Melenk J.M., and Babuska I. The partition of unity finite element method: Basic theory and applications. Comput. Meth. Appl. Mech. Eng. 139 (1996) 289-314
    • (1996) Comput. Meth. Appl. Mech. Eng. , vol.139 , pp. 289-314
    • Melenk, J.M.1    Babuska, I.2
  • 42
    • 56249085908 scopus 로고    scopus 로고
    • Boundary element solution of the two-dimensional sine-Gordon equation using continuous linear
    • Mirzaei D., and Dehghan D. Boundary element solution of the two-dimensional sine-Gordon equation using continuous linear. Eng. Anal. Bound. Elem. 33 (2009) 12-24
    • (2009) Eng. Anal. Bound. Elem. , vol.33 , pp. 12-24
    • Mirzaei, D.1    Dehghan, D.2
  • 43
    • 74149087057 scopus 로고    scopus 로고
    • A. Mohebbi, M. Dehghan, High-order solution of one-dimensional sine-Gordon equation using compact finite difference and DIRKN methods, Math. Comput. Modelling (2009), 10.1016/j.mcm.2009.11.015, in press
    • A. Mohebbi, M. Dehghan, High-order solution of one-dimensional sine-Gordon equation using compact finite difference and DIRKN methods, Math. Comput. Modelling (2009), 10.1016/j.mcm.2009.11.015, in press
  • 45
    • 0016101698 scopus 로고
    • Numerical analysis of vortex motion on Josephson structures
    • Nakajima K., Onodera Y., Nakamura T., and Sato R. Numerical analysis of vortex motion on Josephson structures. J. Appl. Phys. 45 (1974) 4095-4099
    • (1974) J. Appl. Phys. , vol.45 , pp. 4095-4099
    • Nakajima, K.1    Onodera, Y.2    Nakamura, T.3    Sato, R.4
  • 46
    • 0027035536 scopus 로고
    • Generalizing the finite element method: diffuse approximation and diffuse elements
    • Nayroles B., Touzot G., and Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements. Comput. Mech. 10 (1992) 307-318
    • (1992) Comput. Mech. , vol.10 , pp. 307-318
    • Nayroles, B.1    Touzot, G.2    Villon, P.3
  • 47
    • 0001739142 scopus 로고
    • Theory of radial basis function approximation in 1990
    • Light F.W. (Ed)
    • Powell M.J.D. Theory of radial basis function approximation in 1990. In: Light F.W. (Ed). Adv. Numer. Anal. (1992) 303-322
    • (1992) Adv. Numer. Anal. , pp. 303-322
    • Powell, M.J.D.1
  • 48
    • 55549139519 scopus 로고    scopus 로고
    • The binary F-expansion method and its application for solving the (n + 1)-dimensional sine-Gordon equation
    • Rui W., He B., and Long Y. The binary F-expansion method and its application for solving the (n + 1)-dimensional sine-Gordon equation. Commun. Nonlin. Sci. Numer. Simul. 14 (2009) 1245-1258
    • (2009) Commun. Nonlin. Sci. Numer. Simul. , vol.14 , pp. 1245-1258
    • Rui, W.1    He, B.2    Long, Y.3
  • 49
    • 0000246322 scopus 로고    scopus 로고
    • Application of the multiquadric method for numerical solution of elliptic partial differential equations
    • Sharan M., Kansa E.J., and Gupta S. Application of the multiquadric method for numerical solution of elliptic partial differential equations. Appl. Math. Comput. 84 (1997) 275-302
    • (1997) Appl. Math. Comput. , vol.84 , pp. 275-302
    • Sharan, M.1    Kansa, E.J.2    Gupta, S.3
  • 50
    • 18144406135 scopus 로고    scopus 로고
    • Numerical simulation of two-dimensional sine-Gordon solitons via a split cosine scheme
    • Sheng Q., Khaliq A.Q.M., and Voss D.A. Numerical simulation of two-dimensional sine-Gordon solitons via a split cosine scheme. Math. Comput. Simul. 68 (2005) 355-373
    • (2005) Math. Comput. Simul. , vol.68 , pp. 355-373
    • Sheng, Q.1    Khaliq, A.Q.M.2    Voss, D.A.3
  • 51
    • 0037451839 scopus 로고    scopus 로고
    • An analytic study of compactons structures in a class of nonlinear dispersive equations
    • Wazwaz A.M. An analytic study of compactons structures in a class of nonlinear dispersive equations. Math. Comput. Simul. 63 (2003) 35-44
    • (2003) Math. Comput. Simul. , vol.63 , pp. 35-44
    • Wazwaz, A.M.1
  • 52
    • 0037143775 scopus 로고    scopus 로고
    • A point interpolation meshless method based on radial basis functions
    • Wang J.G., and Liu G.R. A point interpolation meshless method based on radial basis functions. Int. J. Numer. Meth. Eng. 54 (2002) 1623-1648
    • (2002) Int. J. Numer. Meth. Eng. , vol.54 , pp. 1623-1648
    • Wang, J.G.1    Liu, G.R.2
  • 53
    • 0037192730 scopus 로고    scopus 로고
    • On the optimal shape parameters of radial basis functions used for 2-D meshless methods
    • Wang J.G., and Liu G.R. On the optimal shape parameters of radial basis functions used for 2-D meshless methods. Comput. Meth. Appl. Math. 191 (2002) 2611-2630
    • (2002) Comput. Meth. Appl. Math. , vol.191 , pp. 2611-2630
    • Wang, J.G.1    Liu, G.R.2
  • 54
    • 0000764217 scopus 로고    scopus 로고
    • Error estimates for interpolation by compactly supported radial basis functions of minimal degree
    • Wendland H. Error estimates for interpolation by compactly supported radial basis functions of minimal degree. J. Approx. Theory 93 (1998) 258-396
    • (1998) J. Approx. Theory , vol.93 , pp. 258-396
    • Wendland, H.1
  • 55
    • 51649133223 scopus 로고
    • Hermite-Birkhoff interpolation of scattered data by radial basis functions
    • Wu Z. Hermite-Birkhoff interpolation of scattered data by radial basis functions. Approx. Theory Appl. 8 (1992) 1-10
    • (1992) Approx. Theory Appl. , vol.8 , pp. 1-10
    • Wu, Z.1
  • 56
    • 0346688073 scopus 로고    scopus 로고
    • Modeling light bullets with the two-dimensional sine-Gordon equation
    • Xin J.X. Modeling light bullets with the two-dimensional sine-Gordon equation. Physica D 135 (2000) 345-368
    • (2000) Physica D , vol.135 , pp. 345-368
    • Xin, J.X.1
  • 57
    • 19744375661 scopus 로고    scopus 로고
    • Parameter determination in a partial differential equation from the overspecified data
    • Dehghan M. Parameter determination in a partial differential equation from the overspecified data. Math. Comput. Modelling 41 (2005) 196-213
    • (2005) Math. Comput. Modelling , vol.41 , pp. 196-213
    • Dehghan, M.1
  • 58
    • 9544239366 scopus 로고    scopus 로고
    • Efficient techniques for the second-order parabolic equation subject to nonlocal specifications
    • Dehghan M. Efficient techniques for the second-order parabolic equation subject to nonlocal specifications. Appl. Numer. Math. 52 (2005) 39-62
    • (2005) Appl. Numer. Math. , vol.52 , pp. 39-62
    • Dehghan, M.1
  • 59
    • 33645276878 scopus 로고    scopus 로고
    • A computational study of the one-dimensional parabolic equation subject to nonclassical boundary specifications
    • Dehghan M. A computational study of the one-dimensional parabolic equation subject to nonclassical boundary specifications. Numer. Methods Partial Differential Equations 22 (2006) 220-257
    • (2006) Numer. Methods Partial Differential Equations , vol.22 , pp. 220-257
    • Dehghan, M.1
  • 60
    • 33749559910 scopus 로고    scopus 로고
    • The one-dimensional heat equation subject to a boundary integral specification
    • Dehghan M. The one-dimensional heat equation subject to a boundary integral specification. Chaos Solitons Fractals 32 (2007) 661-675
    • (2007) Chaos Solitons Fractals , vol.32 , pp. 661-675
    • Dehghan, M.1
  • 61
    • 11144275388 scopus 로고    scopus 로고
    • On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation
    • Dehghan M. On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation. Numer. Methods Partial Differential Equations 21 (2005) 24-040
    • (2005) Numer. Methods Partial Differential Equations , vol.21 , pp. 24-040
    • Dehghan, M.1
  • 62
    • 70249128335 scopus 로고    scopus 로고
    • D. Mirzaei, M. Dehghan, Implementation of meshless LBIE method to the 2D non-linear SG problem, Int. J. Numer. Meth. Eng. (2009), doi:10.1002/nme.2635, in press
    • D. Mirzaei, M. Dehghan, Implementation of meshless LBIE method to the 2D non-linear SG problem, Int. J. Numer. Meth. Eng. (2009), doi:10.1002/nme.2635, in press
  • 63
    • 73449115631 scopus 로고    scopus 로고
    • D. Mirzaei, M. Dehghan, Meshless local Petrov-Galerkin (MLPG) approximation to the two dimensional sine-Gordon equation, J. Comput. Appl. Math. (2009), doi:10.1016/j.cam.2009.11.022, in press
    • D. Mirzaei, M. Dehghan, Meshless local Petrov-Galerkin (MLPG) approximation to the two dimensional sine-Gordon equation, J. Comput. Appl. Math. (2009), doi:10.1016/j.cam.2009.11.022, in press


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.