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SOLVABILITY THE TELEGRAPH EQUATION WITH PURELY INTEGRAL CONDITIONS

Yıl 2013, Cilt: 3 Sayı: 1, 117 - 125, 01.06.2013

Öz

In this paper a numerical technique is developed for the one-dimensional telegraph equation, we prove the existence, uniqueness, and continuous dependence upon the data of solution to a telegraph equation with purely integral conditions. The proofs are based on a priori estimates and Laplace transform method. Finally, we obtain the solution by using a simple and efficient algorithm for numerical solution.

Kaynakça

  • [1] Abramowitz, M., Stegun. I.A.,(1972), Hand book of Mathematical Functions, Dover, New York.
  • [2] Ang, W.T., (2002),A Method of Solution for the One-Dimentional Heat Equation Subject to Nonlocal Conditions, Southeast Asian Bulletin of Mathematics 26 , 185-191.
  • [3] Be¨ılin, S. A., (2001), Existence of solutions for one-dimentional wave nonlocal conditions, Electron. J. Differential Equations , no. 76, 1-8.
  • [4] Bouziani, A., (1996), Probl`emes mixtes avec conditions int´egrales pour quelques ´equations aux d´eriv´ees partielles, Ph.D. thesis, Constantine University.
  • [5] Bouziani, A.,(1996), Mixed problem with boundary integral conditions for a certain parabolic equation, J. Appl. Math. Stochastic Anal. 09 ,no. 3, 323-330.
  • [6] Bouziani, A.,(1997), Solution forte d’un probl`eme mixte avec une condition non locale pour une classe d’´equations hyperboliques [Strong solution of a mixed problem with a nonlocal condition for a class of hyperbolic equations], Acad. Roy. Belg. Bull. Cl. Sci. 8 , 53-70.
  • [7] Bouziani, A., (2000), Strong solution to an hyperbolic evolution problem with nonlocal boundary conditions, Maghreb Math. Rev., 9 , no. 1-2, 71–84.
  • [8] Bouziani, A., (2002), Initial-boundary value problem with nonlocal condition for a viscosity equation, Int. J. Math. & Math. Sci. 30 , no. 6, 327-338.
  • [9] Bouziani, A., (2002), On the solvabiliy of parabolic and hyperbolic problems with a boundary integral condition, Internat. J. Math. & Math. Sci., 31 , 435-447.
  • [10] Bouziani, A., (2002), On a class of nonclassical hyperbolic equations with nonlocal conditions, J. Appl. Math. Stochastic Anal. 15 ,no. 2, 136-153.
  • [11] Bouziani, A.,(2004), Mixed problem with only integral boundary conditions for an hyperbolic equation, Internat. J. Math. & Math. Sci., 26, 1279-1291.
  • [12] Bouziani, A. and Benouar N.,(1996), Probl`eme mixte avec conditions int´egrales pour une classe d’´equations hyperboliques, Bull. Belg. Math. Soc. 3 , 137-145.
  • [13] Bouziani, A. & Merazga N.,(2004), Rothe time-discretization method applied to a quasilinear wave equation subject to integral conditions, Advances in Difference Equations, Vol. 2004, N◦ 3, 211-235.
  • [14] Graver D. P.,(1966), Observing stochastic processes and aproximate transform inversion, Oper. Res. 14, 444-459.
  • [15] Gordeziani, D. G. & Avalishvili, G. A., (2000), Solution of nonlocal problems for one-dimensional oscillations of a medium, Mat. Model. 12 , no. 1, 94–103 (Russian).
  • [16] Hassanzadeh Hassan; Pooladi-Darvish Mehran,(2007), Comparision of different numerical Laplace inversion methods for engineering applications, Appl. Math. Comp. 189 1966-1981.
  • [17] Kac˘ur, J., (1985), Method of Rothe in Evolution Equations, Teubner-Texte zur Mathematik, vol. 80, BSB B. G. Teubner Verlagsgesellschaft, Leipzig.
  • [18] Merad, A., (2011), Adomian Decomposition Method for Solution of Parabolic Equation to Nonlocal Conditions,Int. J. Contemp. Math. Sciences, Vol. 6, , no. 30, 1491 - 1496.
  • [19] Merad, A. & Marhoune, A. L., (2012), Strong Solution for a High Order Boundary Value Problem with Integral condition, Turk. J. Math., doi: 10.3906/math-1105-34 .
  • [20] Mesloub S. & Bouziani, A.,(1999), On a class of singular hyperbolic equation with a weighted integral condition, Int. J. Math. Math. Sci. 22 ), no. 3, 511–519.
  • [21] Mesloub S. and Bouziani, A., (2001), Mixed problem with integral conditions for a certain class of hyperbolic equations, Journal of Applied Mathematics, Vol. 1 , no. 3, 107-116.
  • [22] Pul’kina,L. S.,(1999), A non-local problem with integral conditions for hyperbolic equations, Electron. J. Differential Equations , no. 45, 1–6.
  • [23] Pul’kina,L. S.,(2000), On the solvability in L2 of a nonlocal problem with integral conditions for a hyperbolic equation, Differ. Equ. 36 , no. 2, 316–318.
  • [24] Pul’kina,L. S., (2003),A mixed problem with integral condition for the hyperbolic equation, Matematicheskie Zametki, vol. 74, no. 3, , pp. 435–445.
  • [25] Stehfest,H., (1970), Numerical Inversion of the Laplace Transform, Comm. ACM 13, 47-49.
  • [26] Shruti A.D.,(2010), Numerical Solution for Nonlocal Sobolev-type Differential Equations, Electronic Journal of Differential Equations, Conf. 19 , 75-83.
Yıl 2013, Cilt: 3 Sayı: 1, 117 - 125, 01.06.2013

Öz

Kaynakça

  • [1] Abramowitz, M., Stegun. I.A.,(1972), Hand book of Mathematical Functions, Dover, New York.
  • [2] Ang, W.T., (2002),A Method of Solution for the One-Dimentional Heat Equation Subject to Nonlocal Conditions, Southeast Asian Bulletin of Mathematics 26 , 185-191.
  • [3] Be¨ılin, S. A., (2001), Existence of solutions for one-dimentional wave nonlocal conditions, Electron. J. Differential Equations , no. 76, 1-8.
  • [4] Bouziani, A., (1996), Probl`emes mixtes avec conditions int´egrales pour quelques ´equations aux d´eriv´ees partielles, Ph.D. thesis, Constantine University.
  • [5] Bouziani, A.,(1996), Mixed problem with boundary integral conditions for a certain parabolic equation, J. Appl. Math. Stochastic Anal. 09 ,no. 3, 323-330.
  • [6] Bouziani, A.,(1997), Solution forte d’un probl`eme mixte avec une condition non locale pour une classe d’´equations hyperboliques [Strong solution of a mixed problem with a nonlocal condition for a class of hyperbolic equations], Acad. Roy. Belg. Bull. Cl. Sci. 8 , 53-70.
  • [7] Bouziani, A., (2000), Strong solution to an hyperbolic evolution problem with nonlocal boundary conditions, Maghreb Math. Rev., 9 , no. 1-2, 71–84.
  • [8] Bouziani, A., (2002), Initial-boundary value problem with nonlocal condition for a viscosity equation, Int. J. Math. & Math. Sci. 30 , no. 6, 327-338.
  • [9] Bouziani, A., (2002), On the solvabiliy of parabolic and hyperbolic problems with a boundary integral condition, Internat. J. Math. & Math. Sci., 31 , 435-447.
  • [10] Bouziani, A., (2002), On a class of nonclassical hyperbolic equations with nonlocal conditions, J. Appl. Math. Stochastic Anal. 15 ,no. 2, 136-153.
  • [11] Bouziani, A.,(2004), Mixed problem with only integral boundary conditions for an hyperbolic equation, Internat. J. Math. & Math. Sci., 26, 1279-1291.
  • [12] Bouziani, A. and Benouar N.,(1996), Probl`eme mixte avec conditions int´egrales pour une classe d’´equations hyperboliques, Bull. Belg. Math. Soc. 3 , 137-145.
  • [13] Bouziani, A. & Merazga N.,(2004), Rothe time-discretization method applied to a quasilinear wave equation subject to integral conditions, Advances in Difference Equations, Vol. 2004, N◦ 3, 211-235.
  • [14] Graver D. P.,(1966), Observing stochastic processes and aproximate transform inversion, Oper. Res. 14, 444-459.
  • [15] Gordeziani, D. G. & Avalishvili, G. A., (2000), Solution of nonlocal problems for one-dimensional oscillations of a medium, Mat. Model. 12 , no. 1, 94–103 (Russian).
  • [16] Hassanzadeh Hassan; Pooladi-Darvish Mehran,(2007), Comparision of different numerical Laplace inversion methods for engineering applications, Appl. Math. Comp. 189 1966-1981.
  • [17] Kac˘ur, J., (1985), Method of Rothe in Evolution Equations, Teubner-Texte zur Mathematik, vol. 80, BSB B. G. Teubner Verlagsgesellschaft, Leipzig.
  • [18] Merad, A., (2011), Adomian Decomposition Method for Solution of Parabolic Equation to Nonlocal Conditions,Int. J. Contemp. Math. Sciences, Vol. 6, , no. 30, 1491 - 1496.
  • [19] Merad, A. & Marhoune, A. L., (2012), Strong Solution for a High Order Boundary Value Problem with Integral condition, Turk. J. Math., doi: 10.3906/math-1105-34 .
  • [20] Mesloub S. & Bouziani, A.,(1999), On a class of singular hyperbolic equation with a weighted integral condition, Int. J. Math. Math. Sci. 22 ), no. 3, 511–519.
  • [21] Mesloub S. and Bouziani, A., (2001), Mixed problem with integral conditions for a certain class of hyperbolic equations, Journal of Applied Mathematics, Vol. 1 , no. 3, 107-116.
  • [22] Pul’kina,L. S.,(1999), A non-local problem with integral conditions for hyperbolic equations, Electron. J. Differential Equations , no. 45, 1–6.
  • [23] Pul’kina,L. S.,(2000), On the solvability in L2 of a nonlocal problem with integral conditions for a hyperbolic equation, Differ. Equ. 36 , no. 2, 316–318.
  • [24] Pul’kina,L. S., (2003),A mixed problem with integral condition for the hyperbolic equation, Matematicheskie Zametki, vol. 74, no. 3, , pp. 435–445.
  • [25] Stehfest,H., (1970), Numerical Inversion of the Laplace Transform, Comm. ACM 13, 47-49.
  • [26] Shruti A.D.,(2010), Numerical Solution for Nonlocal Sobolev-type Differential Equations, Electronic Journal of Differential Equations, Conf. 19 , 75-83.
Toplam 26 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

A. Merad Bu kişi benim

A. Bouziani Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2013
Yayımlandığı Sayı Yıl 2013 Cilt: 3 Sayı: 1

Kaynak Göster