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Volumn 26, Issue 1, 2010, Pages 239-252

Numerical solution of hyperbolic telegraph equation using the Chebyshev tau method

Author keywords

Chebyshev polynomials; Hyperbolic equation; Operational matrix; Tau method; Telegraph equation

Indexed keywords


EID: 73449109560     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20442     Document Type: Article
Times cited : (159)

References (36)
  • 1
    • 34247184613 scopus 로고    scopus 로고
    • Unconditionally stable difference schemes for a one‐space‐dimensional linear hyperbolic equation
    • 1 F. Gao and C. Chi, Unconditionally stable difference schemes for a one‐space‐dimensional linear hyperbolic equation, Appl Math Comput 187 ( 2007), 1272–1276.
    • (2007) Appl Math Comput , vol.187 , pp. 1272-1276
    • Gao, F.1    Chi, C.2
  • 2
    • 47049124300 scopus 로고    scopus 로고
    • A numerical method for solving the hyperbolic telegraph equation
    • 2 M. Dehghan and A. Shokri, A numerical method for solving the hyperbolic telegraph equation, Numer Methods Partial Differential Eq 24 ( 2008), 1080–1093.
    • (2008) Numer Methods Partial Differential Eq , vol.24 , pp. 1080-1093
    • Dehghan, M.1    Shokri, A.2
  • 3
    • 50849102362 scopus 로고    scopus 로고
    • High order compact solution of the one‐space‐dimensional linear hyperbolic equation
    • 3 A. Mohebbi and M. Dehghan, High order compact solution of the one‐space‐dimensional linear hyperbolic equation, Numer Methods Partial Differential Eq 24 ( 2008), 1222–1235.
    • (2008) Numer Methods Partial Differential Eq , vol.24 , pp. 1222-1235
    • Mohebbi, A.1    Dehghan, M.2
  • 4
    • 33847786088 scopus 로고    scopus 로고
    • Numerical solution of the one‐dimensional wave equation with an integral condition
    • 4 A. Saadatmandi and M. Dehghan, Numerical solution of the one‐dimensional wave equation with an integral condition, Numer Methods Partial Differential Eq 23 ( 2007), 282–292.
    • (2007) Numer Methods Partial Differential Eq , vol.23 , pp. 282-292
    • Saadatmandi, A.1    Dehghan, M.2
  • 5
    • 85120589084 scopus 로고    scopus 로고
    • Variational iteration method for solving the wave equation subject to an integral conservation condition
    • 5 M. Dehghan and A. Saadatmandi, Variational iteration method for solving the wave equation subject to an integral conservation condition, Chaos Solitons Fractals, to appear.
    • Chaos Solitons Fractals
    • Dehghan, M.1    Saadatmandi, A.2
  • 6
    • 0030216940 scopus 로고    scopus 로고
    • On the use of high order difference methods for the system of one space second order non‐linear hyperbolic equations with variable coefficients
    • 6 R. K. Mohanty, M. K. Jain, and K. George, On the use of high order difference methods for the system of one space second order non‐linear hyperbolic equations with variable coefficients, J Comp Appl Math 72 ( 1996), 421–431.
    • (1996) J Comp Appl Math , vol.72 , pp. 421-431
    • Mohanty, R.K.1    Jain, M.K.2    George, K.3
  • 7
    • 34249826970 scopus 로고    scopus 로고
    • A numerical algorithm for the solution of telegraph equations
    • 7 M. S. El‐Azab and M. El‐Gamel, 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‐Gamel, M.2
  • 8
    • 0004049424 scopus 로고
    • Industrial microwave, Heating
    • 8 A. C. Metaxas and R. J. Meredith, Industrial microwave, Heating, Peter Peregrinus, London, 1993.
    • (1993)
    • Metaxas, A.C.1    Meredith, R.J.2
  • 9
    • 0003445112 scopus 로고
    • Foundations and industrial applications of microwaves and radio frequency fields
    • 9 G. Roussy and J. A. Pearcy, Foundations and industrial applications of microwaves and radio frequency fields, Wiley, New York, 1995.
    • (1995)
    • Roussy, G.1    Pearcy, J.A.2
  • 10
    • 34250888790 scopus 로고    scopus 로고
    • Computing the variable coefficient telegraph equation using a discrete eigenfunctions method
    • 10 R. Aloy, M. C. Casaban, L. A. Caudillo‐Mata, and L. Jodar, Computing the variable coefficient telegraph equation using a discrete eigenfunctions method, Comput Math Appl 54 ( 2007), 448–458.
    • (2007) Comput Math Appl , vol.54 , pp. 448-458
    • Aloy, R.1    Casaban, M.C.2    Caudillo‐Mata, L.A.3    Jodar, L.4
  • 11
    • 0035500142 scopus 로고    scopus 로고
    • An unconditionally stable alternating direction implicit scheme for the two space dimensional linear hyperbolic equation
    • 11 R. K. Mohanty and M. K. Jain, An unconditionally stable alternating direction implicit scheme for the two space dimensional linear hyperbolic equation, Numer Methods Partial Differential Eq 17 ( 2001), 684–688.
    • (2001) Numer Methods Partial Differential Eq , vol.17 , pp. 684-688
    • Mohanty, R.K.1    Jain, M.K.2
  • 12
    • 0942302128 scopus 로고    scopus 로고
    • An unconditionally stable ADI method for the linear hyperbolic equation in three space dimensions
    • 12 R. K. Mohanty, M. K. Jain, and U. Arora, An unconditionally stable ADI method for the linear hyperbolic equation in three space dimensions, 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
  • 13
    • 84874427620 scopus 로고    scopus 로고
    • The state of art in spectral methods
    • 13 B. Y. Guo, The state of art in spectral methods, City University of Hong Kong, Hong Kong, 1996.
    • (1996)
    • Guo, B.Y.1
  • 14
    • 85162699057 scopus 로고
    • Trigonometric interpolation of empirical and analytic functions
    • 14 C. Lanczos, Trigonometric interpolation of empirical and analytic functions, J Math Phys 17 ( 1938), 123–199.
    • (1938) J Math Phys , vol.17 , pp. 123-199
    • Lanczos, C.1
  • 15
    • 0003398168 scopus 로고
    • Applied analysis
    • 15 C. Lanczos, Applied analysis, Pitman, London, 1957.
    • (1957)
    • Lanczos, C.1
  • 17
    • 0021177673 scopus 로고
    • Numerical solution of partial differential equations with variable coefficients with an operational approach to the tau method
    • 17 E. L. Ortiz and H. Samara, Numerical solution of partial differential equations with variable coefficients with an operational approach to the tau method, Comput Math Appl 10 ( 1984), 5–13.
    • (1984) Comput Math Appl , vol.10 , pp. 5-13
    • Ortiz, E.L.1    Samara, H.2
  • 18
    • 0040679523 scopus 로고
    • The algebraic kernel method for the numerical solution of partial differential equations
    • 18 M. H. A. Abadi and E. L. Ortiz, The algebraic kernel method for the numerical solution of partial differential equations, J Numer Funct Anal Optim 12 ( 1991), 339–360.
    • (1991) J Numer Funct Anal Optim , vol.12 , pp. 339-360
    • Abadi, M.H.A.1    Ortiz, E.L.2
  • 19
    • 0003766476 scopus 로고
    • Spectral methods in fluid dynamic
    • 19 C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral methods in fluid dynamic, Prentice‐Hall, Englewood Cliffs, NJ, 1988.
    • (1988)
    • Canuto, C.1    Hussaini, M.Y.2    Quarteroni, A.3    Zang, T.A.4
  • 20
    • 0040679523 scopus 로고
    • The algebraic kernel method for the numerical solution of partial differential equations
    • 20 L. F. Cordero and R. Escalante, The algebraic kernel method for the numerical solution of partial differential equations, J Numer Funct Anal Optim 12 ( 1991), 339–360.
    • (1991) J Numer Funct Anal Optim , vol.12 , pp. 339-360
    • Cordero, L.F.1    Escalante, R.2
  • 21
    • 33846930099 scopus 로고    scopus 로고
    • A tau method for the one‐dimensional parabolic inverse problem subject to temperature overspecification
    • 21 M. Dehghan and A. Saadatmandi, A tau method for the one‐dimensional parabolic inverse problem subject to temperature overspecification, Comput Math Appl 52 ( 2006), 933–940.
    • (2006) Comput Math Appl , vol.52 , pp. 933-940
    • Dehghan, M.1    Saadatmandi, A.2
  • 22
    • 27844498825 scopus 로고    scopus 로고
    • Hartley series approximations for the parabolic equations
    • 22 A. Saadatmandi, M. Razzaghi, and M. Dehghan, Hartley series approximations for the parabolic equations, Int J Comput Math 82 ( 2005), 1149–1156.
    • (2005) Int J Comput Math , vol.82 , pp. 1149-1156
    • Saadatmandi, A.1    Razzaghi, M.2    Dehghan, M.3
  • 23
    • 57749203983 scopus 로고    scopus 로고
    • Numerical solution of a mathematical model for capillary formation in tumor angiogenesis via the tau method
    • 23 A. Saadatmandi and M. Dehghan, Numerical solution of a mathematical model for capillary formation in tumor angiogenesis via the tau method, Commun Numer Methods Eng 24 ( 2008), 1467–1474.
    • (2008) Commun Numer Methods Eng , vol.24 , pp. 1467-1474
    • Saadatmandi, A.1    Dehghan, M.2
  • 24
    • 0037448159 scopus 로고    scopus 로고
    • Chebyshev finite difference approximation for the boundary value problems
    • 24 E. M. E. Elbarbary, Chebyshev finite difference approximation for the boundary value problems, Appl Math Comput 139 ( 2003), 513–523.
    • (2003) Appl Math Comput , vol.139 , pp. 513-523
    • Elbarbary, E.M.E.1
  • 25
    • 0035251701 scopus 로고    scopus 로고
    • Frobenius‐Chebyshev polynomial approximations with a priori error bounds for nonlinear initial value differential problems
    • 25 B. Chen, R. Garcia‐Bolos, and L. Jodar, Frobenius‐Chebyshev polynomial approximations with a priori error bounds for nonlinear initial value differential problems, Comput Math Appl 41 ( 2001), 269–280.
    • (2001) Comput Math Appl , vol.41 , pp. 269-280
    • Chen, B.1    Garcia‐Bolos, R.2    Jodar, L.3
  • 26
    • 0038683230 scopus 로고    scopus 로고
    • The truncation error of the two‐variable Chebyshev series expansions
    • 26 B. Chen, R. Garcia‐Bolos, L. Jodar, and M. D. Rosello, The truncation error of the two‐variable Chebyshev series expansions, Comput Math Appl 45 ( 2003), 1647–1653.
    • (2003) Comput Math Appl , vol.45 , pp. 1647-1653
    • Chen, B.1    Garcia‐Bolos, R.2    Jodar, L.3    Rosello, M.D.4
  • 27
    • 0022101681 scopus 로고
    • Application of shifted Chebyshev series to the optimal control of linear distributed‐parameter systems
    • 27 I. R. Horng and J. H. Chou, Application of shifted Chebyshev series to the optimal control of linear distributed‐parameter systems, Int J Control 42 ( 1985), 233–241.
    • (1985) Int J Control , vol.42 , pp. 233-241
    • Horng, I.R.1    Chou, J.H.2
  • 28
    • 27144506208 scopus 로고    scopus 로고
    • Analytic and approximate solutions of the space and time‐fractional telegraph equations
    • 28 S. Momani, Analytic and approximate solutions of the space and time‐fractional telegraph equations, Appl Math Comput 170 ( 2005), 1126–1134.
    • (2005) Appl Math Comput , vol.170 , pp. 1126-1134
    • Momani, S.1
  • 29
    • 32644435892 scopus 로고    scopus 로고
    • Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices
    • 29 M. Dehghan, 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
  • 30
    • 11144275388 scopus 로고    scopus 로고
    • On the solution of an initial‐boundary value problem that combines Neumann and integral condition for the wave equation
    • 30 M. Dehghan, On the solution of an initial‐boundary value problem that combines Neumann and integral condition for the wave equation, Numer Methods for Partial Differential Eq 21 ( 2005), 24–40.
    • (2005) Numer Methods for Partial Differential Eq , vol.21 , pp. 24-40
    • Dehghan, M.1
  • 31
    • 18744412104 scopus 로고    scopus 로고
    • Identification of a time‐dependent coefficient in a partial differential equation subject to an extra measurement
    • 31 M. Dehghan, Identification of a time‐dependent coefficient in a partial differential equation subject to an extra measurement, Numer Methods for Partial Differential Eq 21 ( 2005), 611–622.
    • (2005) Numer Methods for Partial Differential Eq , vol.21 , pp. 611-622
    • Dehghan, M.1
  • 32
  • 33
    • 33645276878 scopus 로고    scopus 로고
    • A computational study of the one‐dimensional parabolic equation subject to nonclassical boundary specifications
    • 33 M. Dehghan, A computational study of the one‐dimensional parabolic equation subject to nonclassical boundary specifications, Numer Methods for Partial Differential Eq 22 ( 2006), 220–257.
    • (2006) Numer Methods for Partial Differential Eq , vol.22 , pp. 220-257
    • Dehghan, M.1
  • 34
    • 33749559910 scopus 로고    scopus 로고
    • The one‐dimensional heat equation subject to a boundary integral specification
    • 34 M. Dehghan, The one‐dimensional heat equation subject to a boundary integral specification, Chaos, Solitons and Fractals 32 ( 2007), 661–675.
    • (2007) Chaos, Solitons and Fractals , vol.32 , pp. 661-675
    • Dehghan, M.1
  • 35
    • 35448960877 scopus 로고    scopus 로고
    • Numerical solution of the Klein‐Gordon equation via H's variational iteration method
    • 35 F. Shakeri and M. Dehghan, Numerical solution of the Klein‐Gordon equation via H's variational iteration method, Nonlinear Dynamics 51 ( 2008), 89–97.
    • (2008) Nonlinear Dynamics , vol.51 , pp. 89-97
    • Shakeri, F.1    Dehghan, M.2
  • 36
    • 56249086875 scopus 로고    scopus 로고
    • The boundary integral equation approach for numerical solution of the one‐dimensional Sine‐Gordon equation
    • 36 M. Dehghan and D. Mirzaei, The boundary integral equation approach for numerical solution of the one‐dimensional Sine‐Gordon equation, Numer Methods for Partial Differential Eq 24 ( 2008), 1405–1415.
    • (2008) Numer Methods for Partial Differential Eq , vol.24 , pp. 1405-1415
    • Dehghan, M.1    Mirzaei, D.2


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