Laplace ve adomian ayrışma metodları ile Benney-Luke denkleminin çözümünü elde etme

Bu çalışmada, başlangıç değerleri verilen homojen olmayan Benney-Luke denklemini ele aldık. Laplace ve Adomian ayrışma metotları bu denkleme uygulanmıştır. Daha sonra, bu denklemin verilen başlangıç değerini sağlayan çözümü elde edilmiştir.

Obtaining the solution of Benney-Luke Equation by Laplace and adomian decomposition methods

In this study, we consider the inhomogeneous Benney-Luke equation with its initial conditions. Laplace Decomposition Method and Adomian Decomposition Method are applied to this equation. Then, the solution yielding the given initial conditions is gained.

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N. Damil, M. Potier-Ferry, A. Najah, R. Chari, and H. Lahmam, “An iterative method based upon Pade approximamants,” Communication in Numerical Methods in Engineering, vol. 15, pp. 701-708, 1999.
G.-L. Liu, “New research directions in singular perturbation theory: artificial parameter approach and inverseperturbation technique,” Proceeding of the 7th Conference of the Modern Mathematics and Mechanics, Shanghai, pp. 47-53, 1997.
J.-H. He, “A coupling method of homotopy technique and perturbation technique for nonlinear problems,” International Journal Of Non-Linear Mechanics, vol. 35, pp. 37- 43, 2000.
J.-M.Cadou, N. Moustaghfir, E. H. Mallil., N. Damil and M. Potier-Ferry, “Linear iterative solvers based on pertubration techniques,” Comptes Rendus Mathematique, vol. 332, pp. 457-462, 2001.
E. Mallil, H. Lahmam, N. Damil and M. Potier-Ferry, “An iterative process based on homotopy and perturbation techniques,” Computer Methods In Applied Mechanics Engineering, vol. 190, pp. 1845-1858, 2000.
C. M. Bender, K. S. Pinsky and L. M. Simmons, “A new perturbative approach to nonlinear problems,” Journal of mathematical Physics, vol. 30, pp. 1447- 1455, 1989.
G. Adomian, “Nonlinear stochastic systems theory and applications to physics,” in Mathematics And Its Applications, Kluwer Academic Publishers, vol. 46 pp. 10-224, 1989.
G. Adomian, “Solving frontier problems of physics: the decomposition method,” in Fundamental Theories Of Physics, Kluwer Academic Publishers-Plenum, Springer Netherlands, vol. 60, pp. 6-195, 1994.
G. Adomian, “An analytic solution of the stochastic Navier-Stokes system,” in Foundations Of Physics, Kluwer Academic Publisher, Springer Science And Business Media, vol. 21, pp. 831-843, 1991.
G. Adomian, “Solution of physical problems by decomposition,” Computers And Mathematacis with Applications, vol. 27, pp. 145-154, 1994.
G. Adomian, “Solution of nonlinear P.D.E,” Applied Mathematics Letters, vol. 11, pp. 121-123, 1998.
G. Adomian and R. Rach, “Linear and nonlinear Schröndinger equations,” in Foundations Of Physics, Kluwer Academic Publishers-Plenum, vol. 21, pp. 983-991, 1991.
G. Adomian and R. Rach, “Inhomogeneous nonlinear partial differential equations with variable coefficients,” Applied Mathematics Letters, vol. 5, pp. 11-12, 1992.
G. Adomian and R. Rach, “Modified decomposition solutions of nonlinear partial differential equations,” Applied Mathematics Letters, vol. 5, pp. 29-30, 1992.
G.Adomian and R. Rach, “A modified decomposition series,” Computers And Mathematacis with Applications, vol. 23, pp. 17-23, 1992.
S. A. Khuri, “A laplace decomposition algorithm applied to class of nonlinear differential equations,” Journal of Mathematical Analysis And Applications, vol.1, pp. 141-155, 2001.
K. Majid, M. Hussain, J. Hossein and K. Yasir, “Application of Laplace decomposition method to solve nonlinear coupled partial differential equations,” World Applied Sciences Journal, vol. 9, pp. 13-19, 2010.
K. Majid and A. G. Muhammed, “Application of Laplace decomposition to solve nonlinear partial differential equations,” International Journal Of Advanced Research In Computer Science, vol. 2, pp. 52-62, 2010.
H. Hosseinzadeh, H. Jafari and M. Roohani, “Application of Laplace decomposition method for solving Klein-Gordon equation,” World Applied Sciences Journal, vol. 8, pp. 809-813, 2010.
K. Majid and M. Hussain, “Application of Laplace decomposition method on semiinfinite domain,” Numerical Algorithms., vol. 56, pp. 211-218, 2011.
J. R. Quintero and J. C Munoz Grajales, “Instability of solitary waves for a generalized Benney-Luke equation,” Nonlinear Analysis Theory, Methods And Applications, vol. 68, pp. 3009-3033, 2008.
A. M. Wazwaz, “The noise terms phenomenon,” in Partial differential equations and solitary waves theory, Beijing, P. R. China, Higher Education Press, ch. 2, sec. 3, pp. 36-40, 2009.