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Volumn 34, Issue 4, 2010, Pages 324-336

Combination of meshless local weak and strong (MLWS) forms to solve the two dimensional hyperbolic telegraph equation

Author keywords

Collocation method; Meshless local Petrov Galerkin (MLPG) method; Meshless local weak strong (MLWS) form method; Moving least square (MLS) approximation; Two dimensional hyperbolic telegraph equation

Indexed keywords

COLLOCATION METHOD; MESHLESS; MESHLESS LOCAL PETROV-GALERKIN METHOD; MOVING LEAST SQUARE APPROXIMATION; TELEGRAPH EQUATION;

EID: 74449091789     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2009.10.010     Document Type: Article
Times cited : (134)

References (58)
  • 1
    • 0035500142 scopus 로고    scopus 로고
    • An unconditionally stable alternating direction implicit scheme for the two space dimensional linear hyperbolic equation
    • Mohanty R.K., and Jain M.K. An unconditionally stable alternating direction implicit scheme for the two space dimensional linear hyperbolic equation. Numer Meth Partial Diff Eq 7 (2001) 684-688
    • (2001) Numer Meth Partial Diff Eq , vol.7 , pp. 684-688
    • Mohanty, R.K.1    Jain, M.K.2
  • 2
    • 0942302128 scopus 로고    scopus 로고
    • An unconditionally stable ADI method for the linear hyperbolic equation in three space dimensional
    • Mohanty R.K., Jain M.K., and Arora U. An unconditionally stable ADI method for the linear hyperbolic equation in three space dimensional. Int J Comput Math 79 (2002) 133-142
    • (2002) Int J Comput Math , vol.79 , pp. 133-142
    • Mohanty, R.K.1    Jain, M.K.2    Arora, U.3
  • 3
    • 63449085865 scopus 로고    scopus 로고
    • A meshless method for numerical solution of a linear hyperbolic equation with variable coefficients in two space dimensions
    • Dehghan M., and Shokri A. A meshless method for numerical solution of a linear hyperbolic equation with variable coefficients in two space dimensions. Numer Meth Partial Diff Eq 25 (2009) 494-506
    • (2009) Numer Meth Partial Diff Eq , vol.25 , pp. 494-506
    • Dehghan, M.1    Shokri, A.2
  • 4
    • 58449133487 scopus 로고    scopus 로고
    • High order implicit collocation method for the solution of two-dimensional linear hyperbolic equation
    • Dehghan M., and Mohebbi A. High order implicit collocation method for the solution of two-dimensional linear hyperbolic equation. Numer Meth Partial Diff Eq 25 (2009) 232-243
    • (2009) Numer Meth Partial Diff Eq , vol.25 , pp. 232-243
    • Dehghan, M.1    Mohebbi, A.2
  • 5
    • 73449109560 scopus 로고    scopus 로고
    • Numerical solution of hyperbolic telegraph equation using the Chebyshev tau method
    • in press, DOI 10.1002/num.20442
    • Saadatmandi A, Dehghan M. Numerical solution of hyperbolic telegraph equation using the Chebyshev tau method. Numer Meth Partial Diff Eq 2008; DOI 10.1002/num.20442 [in press].
    • (2008) Numer Meth Partial Diff Eq
    • Saadatmandi, A.1    Dehghan, M.2
  • 6
    • 33745832661 scopus 로고    scopus 로고
    • Asymptotic solution of wave front of the telegraph model of dispersive variability
    • Abdusalam A.H. Asymptotic solution of wave front of the telegraph model of dispersive variability. Chaos, Solitons Fractals 30 (2006) 1190-1197
    • (2006) Chaos, Solitons Fractals , vol.30 , pp. 1190-1197
    • Abdusalam, A.H.1
  • 7
    • 34249826970 scopus 로고    scopus 로고
    • A numerical algorithm for the solution of telegraph equations
    • El-Azab M.S., and El-Ghamel M. A numerical algorithm for the solution of telegraph equations. Appl Math Comput 190 (2007) 757-764
    • (2007) Appl Math Comput , vol.190 , pp. 757-764
    • El-Azab, M.S.1    El-Ghamel, M.2
  • 10
    • 70349919225 scopus 로고    scopus 로고
    • New unconditionally stable difference schemes for the solution of multi-dimensional telegraphic equations
    • Mohanty RK. New unconditionally stable difference schemes for the solution of multi-dimensional telegraphic equations, Int J Comput Math 2008:1-11.
    • (2008) Int J Comput Math , pp. 1-11
    • Mohanty, R.K.1
  • 11
    • 50849102362 scopus 로고    scopus 로고
    • High order compact solution of the one-space-dimensional linear hyperbolic equation
    • Mohebbi A., and Dehghan M. High order compact solution of the one-space-dimensional linear hyperbolic equation. Numer Meth Partial Diff Eq 24 (2008) 1222-1235
    • (2008) Numer Meth Partial Diff Eq , vol.24 , pp. 1222-1235
    • Mohebbi, A.1    Dehghan, M.2
  • 12
    • 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
  • 14
    • 33748938323 scopus 로고    scopus 로고
    • Implicit collocation technique for heat equation with non-classic initial condition
    • Dehghan M. Implicit collocation technique for heat equation with non-classic initial condition. Int J Nonlinear Sci Numer Simul 7 (2006) 461-466
    • (2006) Int J Nonlinear Sci Numer Simul , vol.7 , pp. 461-466
    • Dehghan, M.1
  • 15
    • 84903913337 scopus 로고
    • Approximations to functions and to the solutions of differential equations. Great Britain Aero Counc. London
    • Rep. and Memo
    • Frazer RA, Jones WP, Skan SW. Approximations to functions and to the solutions of differential equations. Great Britain Aero Counc. London. Rep. and Memo, 1937.
    • (1937)
    • Frazer, R.A.1    Jones, W.P.2    Skan, S.W.3
  • 16
    • 85162699057 scopus 로고
    • Trigonometric interpolation of empirical and analytical functions
    • Lanczos C. Trigonometric interpolation of empirical and analytical functions. J Math Phys 17 (1938) 123-199
    • (1938) J Math Phys , vol.17 , pp. 123-199
    • Lanczos, C.1
  • 17
    • 11644251030 scopus 로고
    • Electronic energy bands in metals
    • Slater J.C. Electronic energy bands in metals. Phys Rev 45 (1934) 794-801
    • (1934) Phys Rev , vol.45 , pp. 794-801
    • Slater, J.C.1
  • 18
    • 0001535601 scopus 로고
    • A deterministic vortex sheet method for boundary layer flow
    • Bernard P.S. A deterministic vortex sheet method for boundary layer flow. J Comput Phys 117 (1995) 132-145
    • (1995) J Comput Phys , vol.117 , pp. 132-145
    • Bernard, P.S.1
  • 19
    • 0347786769 scopus 로고
    • Numerical study of slightly viscous flow
    • Chorin A.J. Numerical study of slightly viscous flow. J Fluid Mech 57 (1937) 785-796
    • (1937) J Fluid Mech , vol.57 , pp. 785-796
    • Chorin, A.J.1
  • 20
    • 0016047189 scopus 로고
    • Theory of a GDM on irregular networks
    • Girault V. Theory of a GDM on irregular networks. SIAM J Numer Anal 11 (1974) 260-282
    • (1974) SIAM J Numer Anal , vol.11 , pp. 260-282
    • Girault, V.1
  • 21
    • 74449084061 scopus 로고
    • Finite difference energy techniques for arbitrary meshes
    • Pavlin V., and Perrone N. Finite difference energy techniques for arbitrary meshes. Comput Struct 5 (1975) 45-58
    • (1975) Comput Struct , vol.5 , pp. 45-58
    • Pavlin, V.1    Perrone, N.2
  • 22
    • 0019606280 scopus 로고
    • The application of a general FDM to some boundary value problems
    • Snell C., Vesey D.G., and Mullord P. The application of a general FDM to some boundary value problems. Comput Struct 13 (1981) 547-552
    • (1981) Comput Struct , vol.13 , pp. 547-552
    • Snell, C.1    Vesey, D.G.2    Mullord, P.3
  • 23
    • 0035440759 scopus 로고    scopus 로고
    • A finite point method for elasticity problems
    • Onate E., Perazzo F., and Miquel J. A finite point method for elasticity problems. Comput Struct 79 (2001) 2151-2163
    • (2001) Comput Struct , vol.79 , pp. 2151-2163
    • Onate, E.1    Perazzo, F.2    Miquel, J.3
  • 24
    • 0030294780 scopus 로고    scopus 로고
    • A finite point method in computational mechanics, applications to convective transport and fluid flow
    • Onate E., Idelsohn S., Zienkiewicz O.Z., and Taylor R.L. A finite point method in computational mechanics, applications to convective transport and fluid flow. Int J Numer Meth Eng 39 (1996) 3839-3867
    • (1996) Int J Numer Meth Eng , vol.39 , pp. 3839-3867
    • Onate, E.1    Idelsohn, S.2    Zienkiewicz, O.Z.3    Taylor, R.L.4
  • 26
    • 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 (1990) 127-145
    • (1990) Comput Math Appl , vol.19 , pp. 127-145
    • Kansa, E.J.1
  • 27
    • 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
  • 28
    • 0034294250 scopus 로고    scopus 로고
    • Meshless methods based on collocation with radial basis functions
    • Zhang X., Song K.Z., Lu M.W., and Liu X. Meshless methods based on collocation with radial basis functions. Comput Mech 26 (2000) 333-343
    • (2000) Comput Mech , vol.26 , pp. 333-343
    • Zhang, X.1    Song, K.Z.2    Lu, M.W.3    Liu, X.4
  • 29
    • 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
  • 30
    • 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 (1998) 187-196
    • (1998) Comput Model Simul Eng , vol.3 , pp. 187-196
    • Atluri, S.N.1    Zhu, T.2
  • 31
    • 0001081434 scopus 로고    scopus 로고
    • New concepts in meshless methods
    • Atluri S.N., and Zhu T. New concepts in meshless methods. Comput Mech 22 (2000) 117-127
    • (2000) Comput Mech , vol.22 , pp. 117-127
    • Atluri, S.N.1    Zhu, T.2
  • 32
    • 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
  • 33
    • 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
  • 34
    • 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
  • 35
    • 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
  • 36
    • 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
  • 38
    • 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
  • 39
    • 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
  • 40
    • 0032436773 scopus 로고    scopus 로고
    • Modeling confined multi-material heat and mass flows using SPH
    • Clear P.W. Modeling confined 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
  • 41
    • 0029102512 scopus 로고
    • Reproducing kernel particle methods
    • Liu W.K., Jun S., and Zhang Y.F. Reproducing kernel particle methods. Int J Numer Meth Eng 20 (1995) 1081-1106
    • (1995) Int J Numer Meth Eng , vol.20 , pp. 1081-1106
    • Liu, W.K.1    Jun, S.2    Zhang, Y.F.3
  • 42
    • 0031104069 scopus 로고    scopus 로고
    • Boundary node method for potential problems
    • Mukherjee Y.X., and Mukherjee S. Boundary node method for potential problems. Int J Numer Meth Eng 40 (1997) 797-815
    • (1997) Int J Numer Meth Eng , vol.40 , pp. 797-815
    • Mukherjee, Y.X.1    Mukherjee, S.2
  • 43
    • 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
  • 44
    • 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
  • 45
    • 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
  • 46
    • 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, An International Journal 15 5 (2003) 535-550
    • (2003) Struct Eng Mech, An International Journal , vol.15 , Issue.5 , pp. 535-550
    • Gu, Y.T.1    Liu, G.R.2
  • 47
    • 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
  • 48
    • 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
  • 49
    • 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
  • 50
    • 10844229274 scopus 로고    scopus 로고
    • A meshfree weak-strong (MWS) form method for time dependent problems
    • Gu Y.T., and Liu G.R. A meshfree weak-strong (MWS) form method for time dependent problems. Comput Mech 35 (2005) 134-145
    • (2005) Comput Mech , vol.35 , pp. 134-145
    • Gu, Y.T.1    Liu, G.R.2
  • 51
    • 3042847440 scopus 로고    scopus 로고
    • A meshfree method: meshfree weak strong (MWS) form method, for 2-D solids
    • Liu G.R., and Gu Y.T. A meshfree method: meshfree weak strong (MWS) form method, for 2-D solids. Comput Mech 33 (2003) 2-14
    • (2003) Comput Mech , vol.33 , pp. 2-14
    • Liu, G.R.1    Gu, Y.T.2
  • 52
    • 9744222922 scopus 로고    scopus 로고
    • Meshfree weak strong (MWS) form method and its application to incompressible flow problems
    • Liu G.R., Wu Y.L., and Ding H. Meshfree weak strong (MWS) form method and its application to incompressible flow problems. Int J Numer Meth Fluids 46 10 (2004) 1025-1047
    • (2004) Int J Numer Meth Fluids , vol.46 , Issue.10 , pp. 1025-1047
    • Liu, G.R.1    Wu, Y.L.2    Ding, H.3
  • 53
    • 84966237423 scopus 로고
    • Surfaces generated by moving least squares methods
    • Lancaster P., and Salkauskas K. Surfaces generated by moving least squares methods. Math Comput 37 (1981) 141-158
    • (1981) Math Comput , vol.37 , pp. 141-158
    • Lancaster, P.1    Salkauskas, K.2
  • 54
    • 0030571226 scopus 로고    scopus 로고
    • Smoothing and accelerated computations in the element free Galerkin method
    • Belytschko T., Krongauz Y., Organ D., and Liu W.K. Smoothing and accelerated computations in the element free Galerkin method. J Comput Appl Math 74 (1996) 111-126
    • (1996) J Comput Appl Math , vol.74 , pp. 111-126
    • Belytschko, T.1    Krongauz, Y.2    Organ, D.3    Liu, W.K.4
  • 55
    • 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
  • 56
    • 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
  • 57
    • 0033908369 scopus 로고    scopus 로고
    • New concepts in meshless methods
    • Atluri S.N., and Zhu T. New concepts in meshless methods. Int J Numer Meth Eng 47 (2000) 537-556
    • (2000) Int J Numer Meth Eng , vol.47 , pp. 537-556
    • Atluri, S.N.1    Zhu, T.2
  • 58
    • 67349149620 scopus 로고    scopus 로고
    • A new fourth-order compact finite difference scheme for the two-dimensional second-order hyperbolic equation
    • Ding H., and Zhang Y. A new fourth-order compact finite difference scheme for the two-dimensional second-order hyperbolic equation. J Comput Appl Math 230 (2009) 626-632
    • (2009) J Comput Appl Math , vol.230 , pp. 626-632
    • Ding, H.1    Zhang, Y.2


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