메뉴 건너뛰기




Volumn 51, Issue 1-2, 2008, Pages 89-97

Numerical solution of the Klein-Gordon equation via He's variational iteration method

Author keywords

Klein Gordon equation; Mesh points schemes; Quantum mechanics; Small perturbations; Variational iteration method

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS; LAGRANGE MULTIPLIERS; PERTURBATION TECHNIQUES; PROBLEM SOLVING;

EID: 35448960877     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-006-9194-x     Document Type: Article
Times cited : (124)

References (36)
  • 2
    • 0002079274 scopus 로고
    • Analysis of four numerical schemes for a nonlinear Klein-Gordon equation
    • 1
    • Jiménez, S., Vázquez, L.: Analysis of four numerical schemes for a nonlinear Klein-Gordon equation. Appl. Math. Comput. 35(1), 61-94 (1990)
    • (1990) Appl. Math. Comput. , vol.35 , pp. 61-94
    • Jiménez, S.1    Vázquez, L.2
  • 3
    • 0033208009 scopus 로고    scopus 로고
    • Large amplitude instability in finite difference approximations to the Klein-Gordon equation
    • 2
    • Lynch, M.A.M.: Large amplitude instability in finite difference approximations to the Klein-Gordon equation. Appl. Numer. Math. 31(2), 173-182 (1999)
    • (1999) Appl. Numer. Math. , vol.31 , pp. 173-182
    • Lynch, M.A.M.1
  • 4
    • 0003775898 scopus 로고
    • Numerical solution for nonlinear Klein-Gordon equation by collocation method with respect to spectral method
    • 3
    • Lee, I.J.: Numerical solution for nonlinear Klein-Gordon equation by collocation method with respect to spectral method. J. Korean Math. Soc. 32(3), 541-551 (1995)
    • (1995) J. Korean Math. Soc. , vol.32 , pp. 541-551
    • Lee, I.J.1
  • 5
    • 0003102674 scopus 로고    scopus 로고
    • An initial-boundary value problem of a nonlinear Klein-Gordon equation
    • 1
    • Wong, Y.S., Chang, Q., Gong, L.: An initial-boundary value problem of a nonlinear Klein-Gordon equation. Appl. Math. Comput. 84(1), 77-93 (1997)
    • (1997) Appl. Math. Comput. , vol.84 , pp. 77-93
    • Wong, Y.S.1    Chang, Q.2    Gong, L.3
  • 6
    • 33748770926 scopus 로고    scopus 로고
    • Global solutions for nonlinear Klein-Gordon equations in infinite homogeneous wave guides
    • Fang, D., Zhong, S.: Global solutions for nonlinear Klein-Gordon equations in infinite homogeneous wave guides. J. Differ. Equ. 231, 212-234 (2006)
    • (2006) J. Differ. Equ. , vol.231 , pp. 212-234
    • Fang, D.1    Zhong, S.2
  • 7
    • 23444443210 scopus 로고    scopus 로고
    • Nonlinear hyperbolic equations in infinite homogeneous wave guides
    • 4-6
    • Metcalfe, J., Sogge, C.D., Stewart, A.: Nonlinear hyperbolic equations in infinite homogeneous wave guides. Comm. Partial Differ. Equ. 30(4-6), 643-661 (2005)
    • (2005) Comm. Partial Differ. Equ. , vol.30 , pp. 643-661
    • Metcalfe, J.1    Sogge, C.D.2    Stewart, A.3
  • 8
    • 84990619688 scopus 로고
    • Global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions
    • Klainerman, S.: Global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions. Comm. Pure Appl. Math. 38, 631-641 (1985)
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 631-641
    • Klainerman, S.1
  • 9
    • 33747332288 scopus 로고    scopus 로고
    • Auxiliary equation method and new solutions of Klein-Gordon equations
    • Sirendaoreji, S.: Auxiliary equation method and new solutions of Klein-Gordon equations. Chaos, Solitons Fractals 31, 943-950 (2007)
    • (2007) Chaos, Solitons Fractals , vol.31 , pp. 943-950
    • Sirendaoreji, S.1
  • 10
    • 0037434494 scopus 로고    scopus 로고
    • Compactons in discrete nonlinear Klein-Gordon models
    • Kevrekidis, P.G., Konotop, V.V.: Compactons in discrete nonlinear Klein-Gordon models. Math. Comput. Simul. 62, 79-89 (2003)
    • (2003) Math. Comput. Simul. , vol.62 , pp. 79-89
    • Kevrekidis, P.G.1    Konotop, V.V.2
  • 11
    • 9644301161 scopus 로고    scopus 로고
    • A numerical solution to Klein-Gordon equation with Dirichlet boundary condition
    • Khalifa, M.E., Elgamal, M.: A numerical solution to Klein-Gordon equation with Dirichlet boundary condition. Appl. Math. Comput. 160, 451-475 (2005)
    • (2005) Appl. Math. Comput. , vol.160 , pp. 451-475
    • Khalifa, M.E.1    Elgamal, M.2
  • 12
    • 0003278399 scopus 로고
    • Infinite-dimensional dynamical systems in mechanics and physics
    • Springer-Verlag
    • Temam, R.: Infinite-dimensional dynamical systems in mechanics and physics. Appl. Math. Sci. 68, Springer-Verlag (1988)
    • (1988) Appl. Math. Sci. , vol.68
    • Temam, R.1
  • 13
    • 10444286668 scopus 로고    scopus 로고
    • Numerical solution of damped nonlinear Klein-Gordon equations using variational method and finite element approach
    • Wang, Q., Cheng, D.: Numerical solution of damped nonlinear Klein-Gordon equations using variational method and finite element approach. Appl. Math. Comput. 162, 381-401 (2005)
    • (2005) Appl. Math. Comput. , vol.162 , pp. 381-401
    • Wang, Q.1    Cheng, D.2
  • 14
    • 0007140364 scopus 로고    scopus 로고
    • A new approach to nonlinear partial differential equations
    • 4
    • He, J.H.: A new approach to nonlinear partial differential equations. Commun. Nonlinear Sci. Numer. Simul. 2(4), 230-235 (1997)
    • (1997) Commun. Nonlinear Sci. Numer. Simul. , vol.2 , pp. 230-235
    • He, J.H.1
  • 15
    • 0032307661 scopus 로고    scopus 로고
    • Approximate solution of nonlinear differential equations with convolution product nonlinearities
    • He, J.H.: Approximate solution of nonlinear differential equations with convolution product nonlinearities. Comput. Methods Appl. Mech. Eng. 167, 57-68 (1998)
    • (1998) Comput. Methods Appl. Mech. Eng. , vol.167 , pp. 57-68
    • He, J.H.1
  • 16
    • 19144365030 scopus 로고    scopus 로고
    • Variational iteration method for solving Burgers' and coupled Burgers' equations
    • Abdou, M.A., Soliman, A.A.: Variational iteration method for solving Burgers' and coupled Burgers' equations. J. Comput. Appl. Math. 181, 245-251 (2005)
    • (2005) J. Comput. Appl. Math. , vol.181 , pp. 245-251
    • Abdou, M.A.1    Soliman, A.A.2
  • 17
    • 0141525039 scopus 로고    scopus 로고
    • A new approach to Bratu's problem
    • 1
    • Khuri, S.A.: A new approach to Bratu's problem. Appl. Math. Comput. 147(1), 131-136 (2004)
    • (2004) Appl. Math. Comput. , vol.147 , pp. 131-136
    • Khuri, S.A.1
  • 18
    • 30344475545 scopus 로고    scopus 로고
    • Construction of solitary solution and compacton-like solution by variational iteration method
    • He, J.H., Wu, X.H.: Construction of solitary solution and compacton-like solution by variational iteration method. Chaos, Solitons Fractals 29, 108-113 (2006)
    • (2006) Chaos, Solitons Fractals , vol.29 , pp. 108-113
    • He, J.H.1    Wu, X.H.2
  • 19
    • 85126469460 scopus 로고    scopus 로고
    • Variational iteration method for solving generalized Burgers-Fisher and Burgers equations
    • in press
    • Moghimi, M., Hejazi, F.S.A.: Variational iteration method for solving generalized Burgers-Fisher and Burgers equations. Chaos, Solitons Fractals (in press)
    • Chaos, Solitons Fractals
    • Moghimi, M.1    Hejazi, F.S.A.2
  • 20
    • 24144475568 scopus 로고    scopus 로고
    • Numerical simulation of the generalized regularized long wave equation by He's variational iteration method
    • Soliman, A.A.: Numerical simulation of the generalized regularized long wave equation by He's variational iteration method. Math. Comput. Simul. 70, 119-124 (2005)
    • (2005) Math. Comput. Simul. , vol.70 , pp. 119-124
    • Soliman, A.A.1
  • 21
    • 27144467065 scopus 로고    scopus 로고
    • New applications of variational iteration method
    • Abdou, M.A., Soliman, A.A.: New applications of variational iteration method. Physica D 211, 1-8 (2005)
    • (2005) Physica D , vol.211 , pp. 1-8
    • Abdou, M.A.1    Soliman, A.A.2
  • 22
    • 35448950759 scopus 로고    scopus 로고
    • Numerical solutions of nonlinear evolution equations using variational iteration method
    • in press
    • Soliman A.A., Abdou, M.A. : Numerical solutions of nonlinear evolution equations using variational iteration method. J. Comput. Appl. Math. (in press) A1
    • J. Comput. Appl. Math.
    • Soliman, A.A.1    Abdou, M.A.2
  • 23
    • 24944574717 scopus 로고    scopus 로고
    • The solution of a nonclassic problem for one-dimensional hyperbolic equation using the decomposition procedure
    • Dehghan, M.: The solution of a nonclassic problem for one-dimensional hyperbolic equation using the decomposition procedure. Int. J. Comput. Math. 81, 979-989 (2004)
    • (2004) Int. J. Comput. Math. , vol.81 , pp. 979-989
    • Dehghan, M.1
  • 24
    • 35448930632 scopus 로고    scopus 로고
    • The variational iteration method for rational solutions for KdV, K(2, 2), Burgers, and cubic Boussinesq equations
    • in press
    • Wazwaz, A.M.: The variational iteration method for rational solutions for KdV, K(2, 2), Burgers, and cubic Boussinesq equations. J. Comput. Appl. Math. (in press) A1
    • J. Comput. Appl. Math.
    • Wazwaz, A.M.1
  • 25
    • 35449007975 scopus 로고    scopus 로고
    • Harmonic wave generation in non linear thermoelasticity by variational iteration method and Adomian's method
    • in press
    • Sweilam, N.H.: Harmonic wave generation in non linear thermoelasticity by variational iteration method and Adomian's method. J. Comput. Appl. Math. (in press) A1
    • J. Comput. Appl. Math.
    • Sweilam, N.H.1
  • 26
    • 35448958744 scopus 로고    scopus 로고
    • Solution of problems in calculus of variations via He's variational iteration method
    • accepted
    • Tatari, M., Dehghan, M.: Solution of problems in calculus of variations via He's variational iteration method. Phys. Lett. A (accepted) A1
    • Phys. Lett. A
    • Tatari, M.1    Dehghan, M.2
  • 27
    • 78650193458 scopus 로고    scopus 로고
    • Identifying an unknown function in a parabolic equation with overspecified data via He's variational iteration method
    • in press
    • Dehghan, M., Tatari, M.: Identifying an unknown function in a parabolic equation with overspecified data via He's variational iteration method. Chaos, Solitons Fractals (in press) A1
    • Chaos, Solitons Fractals
    • Dehghan, M.1    Tatari, M.2
  • 28
    • 0006990947 scopus 로고    scopus 로고
    • Variational iteration method for delay differential equations
    • 4
    • He, J.H.: Variational iteration method for delay differential equations. Commun. Nonlinear Sci. Numer. Simul. 2(4), 235-236 (1997)
    • (1997) Commun. Nonlinear Sci. Numer. Simul. , vol.2 , pp. 235-236
    • He, J.H.1
  • 29
    • 0040184009 scopus 로고    scopus 로고
    • Variational iteration method for autonomous ordinary differential systems
    • He, J.H.: Variational iteration method for autonomous ordinary differential systems. Appl. Math. Comput. 114, 115-123 (2000)
    • (2000) Appl. Math. Comput. , vol.114 , pp. 115-123
    • He, J.H.1
  • 30
    • 16844373404 scopus 로고    scopus 로고
    • Approximate analytical solution of Blasius' equation
    • 1
    • He, J.H.: Approximate analytical solution of Blasius' equation. Commun. Nonlinear Sci. Numer. Simul. 4(1), 75-78 (1999)
    • (1999) Commun. Nonlinear Sci. Numer. Simul. , vol.4 , pp. 75-78
    • He, J.H.1
  • 31
    • 35448991566 scopus 로고    scopus 로고
    • On the convergence of He's variational iteration method
    • in press
    • Tatari, M., Dehghan, M.: On the convergence of He's variational iteration method. J. Comput. Appl. Math. (in press) A1
    • J. Comput. Appl. Math.
    • Tatari, M.1    Dehghan, M.2
  • 32
    • 35448975936 scopus 로고    scopus 로고
    • Solving nonlinear partial differential equations using the modified variational iteration Pade technique
    • in press
    • Abassy, T.A., El-Tawil, M.A., El Zoheiryb, H.: Solving nonlinear partial differential equations using the modified variational iteration Pade technique. J. Comput. Appl. Math. (in press) A1
    • J. Comput. Appl. Math.
    • Abassy, T.A.1    El-Tawil, M.A.2    El Zoheiryb, H.3
  • 34
    • 33645972898 scopus 로고    scopus 로고
    • Some asymptotic methods for strongly nonlinear equations
    • 10
    • He, J.H.: Some asymptotic methods for strongly nonlinear equations. Int. J. Modern Phys. B 20(10), 1141-1199 (2006)
    • (2006) Int. J. Modern Phys. B , vol.20 , pp. 1141-1199
    • He, J.H.1
  • 35
    • 32644435892 scopus 로고    scopus 로고
    • Finite difference procedueres for solving a problem arising in modeling and design of certain optoelectronic devices
    • Dehghan, M.: Finite difference procedueres for solving a problem arising in modeling and design of certain optoelectronic devices. Math. Comput. Simul. 71, 16-30 (2006)
    • (2006) Math. Comput. Simul. , vol.71 , pp. 16-30
    • Dehghan, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.