107
Views
35
CrossRef citations to date
0
Altmetric
Miscellany

The solution of a nonclassic problem for one-dimensional hyperbolic equation using the decomposition procedure

Pages 979-989 | Accepted 24 Mar 2004, Published online: 25 Jan 2007

References

References

  • Bouziani , A . (2002) . Initial–Boundary value problem with a nonlocal condition for a viscosity equation . International Journal of Mathematics and Mathematical Science , 30 (6) : 327 – 338 .
  • Capasso , V and Kunisch , K . (1988) . A reaction-diffusion system arising in modelling man-environment diseases . Quart. Appl. Math. , 46 : 431 – 449 .
  • Carlson DE (1972) Linear thermoelasticity Encyclopedia of physics 2 Springer Berlin
  • Cushman , JH and Ginn , TR . (1993) . Nonlocal dispersion in media with continuously evolving scales of heterogeneity . Transport Porous Media , 13 : 123 – 138 .
  • Cushman , JH , Xu , H and Deng , F . (1995) . Nonlocal reactive transport with physical and chemical heterogeneity: Localization error . Water Resource Res. , 31 : 2219 – 2237 .
  • Gordeziani , IS and Avalishvili , GA . (2000) . on the constructing of solutions of the nonlocal initial–boundary problems for one-dimensional medium oscillation equations . Matem. Modelirovanie , 12 (1) : 94 – 103 .
  • Nakhushev , AM . (1982) . On certain approximate method for boundary-value problems for differential equations and its applications in ground waters dynamics . Differentsialnie Uravnenia , 18 : 72 – 81 .
  • Paneiah , BP . (1984) . On certain nonlocal boundary value problems for linear differential operators . Matem. Zametki. , 35 (3) : 425 – 434 .
  • Renardy M Hrusa W Nohel JA (1987) Mathematical problems in viscoelasticity Longman Sci. Tech. England
  • Dehghan M Numerical schemes for one-dimensional parabolic equations with nonstandard initial condition Applied Mathematics and Computation in press
  • Deng , K . (1992) . Comparison principle for some nonlocal problems . Quart. Appl. Math. , 50 : 517 – 522 .
  • Gushin , AK and Mikhailov , VP . (1994) . On solvability of nonlocal problems for second-order elliptic equation . Matem. Sbornik. , 185 : 121 – 160 .
  • Mesloub , S and Bouziani , A . (1999) . On a class of singular hyperbolic equation with a weighted integral condition . Intern. J. Math. and Math. Sci. , 22 : 511 – 520 .
  • Murthy , ASV and Verwer , JG . (1992) . Solving parabolic integro-differential equations by an explicit integration method . J. Comput. Appl. Math. , 39 : 121 – 132 .
  • Beilin , SA . (2001) . Existence of solutions for one-dimensional wave equations with nonlocal conditions . Electronic Journal of Differential Equations , 76 : 1 – 8 .
  • Bouziani , A . (1994) . Mixed problem for certain nonclassical equations containing a small parameter . Acad. Roy. Belg. Bull. CI, Sci. , 6 ( 5 ) : 389 – 400 .
  • Dehghan , M . (2005) . On the solution of an initial–boundary value problem which combine Neumann and integral condition for wave equation . Numerical Methods for Partial Differential Equations , 21 : 1 – 17 .
  • Pulkina , LS . (1999) . A nonlocal problem with integral conditions for hyperbolic equations . Electronic Journal of Differential Equations , 45 : 1 – 6 .
  • Pulkina , LS . (2000) . On solvability in L 2of nonlocal problem with integral conditions for hyperbolic equations . Differets Uravn. V. N. , 2 : 1 – 6 .
  • Dehghan M Efficient techniques for the second-order parabolic equation subject to nonlocal specifications Applied Numerical Mathematics in press.
  • Adomian G (1994) Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Boston
  • Adomian , G . (1988) . A review of the decomposition method in applied mathematics . J. Math. Anal. Appl. , 135 : 501 – 544 .
  • Adomian , G . (1987) . Modification of the decomposition approach to the heat equation . J. Math. Anal. Appl. , 124 : 290 – 291 .
  • Adomian , G . (1986) . A new approach to the heat equation, an application of the decomposition method . J. Math. Anal. Appl. , 113 : 202 – 209 .
  • Adomian , G . (1991) . Solving frontier problems modelled by nonlinear partial differential equations . Comput. Math. Appl. , 22 : 91 – 94 .
  • Kaya , D . (2000) . An application of the decomposition method to the second-order wave equation . Internat. J. Comput. Math. , 75 : 235 – 245 .
  • Lesnic , D . (2001) . A computational algebraic investigation of the decomposition method for time-dependent problems . Appl. Math. Comput , 119 : 197 – 206 .
  • Wazwaz , AM . (1999) . A reliable modification of Adomian decomposition method . Appl. Math. Comput. , 102 : 77 – 86 .
  • Yee , E . (1993) . Application of the decomposition method to the solution of the reaction-convection-diffusion equation . Appl. Math. Comput. , 56 : 1 – 27 .
  • Datta , BK . (1989) . A new approach to the wave equation . J. Math. Anal. Appl. , 142 : 6 – 12 .
  • Cherruault , Y . (1990) . Convergence of Adomian's method . Math. Comput. Modelling , 14 : 83 – 86 .
  • Cherruault , Y . (1993) . G. Adomian decomposition method, A new proof of convergence . Math. Comput. Modelling , 18 ( 12 ) : 103 – 106 .
  • Cherruault , Y and Saccamandi , G . (1992) . Some new results for convergence of Adomian's method applied to integral equations . Math. Comput. Model. , 16 : 83 – 93 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.