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

Year 2017, Volume: 21 Issue: 6, 1524 - 1528, 01.12.2017

Hami Gündoğdu Ömer Faruk Gözükızıl

https://doi.org/10.16984/saufenbilder.340379

Abstract

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.

Keywords

Laplace Decomposition Method Adomian Decomposition Method Benney-Luke Equation The Noise terms

References

  • Referans1 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.
  • Referans2 G.-L. Liu, “New research directions in singular perturbation theory: artificial parameter approach and inverse-perturbation technique,” Proceeding of the 7th Conference of the Modern Mathematics and Mechanics, Shanghai, pp. 47-53, 1997.
  • Referans3 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.
  • Referans4 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.
  • Referans5 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.
  • Referans6 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.
  • Referans7 G. Adomian, “Nonlinear stochastic systems theory and applications to physics,” in Mathematics And Its Applications, Kluwer Academic Publishers, vol. 46 pp. 10-224, 1989.
  • Referans8 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.
  • Referans9 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.
  • Referans10 G. Adomian, “Solution of physical problems by decomposition,” Computers And Mathematacis with Applications, vol. 27, pp. 145-154, 1994.
  • Referans11 G. Adomian, “Solution of nonlinear P.D.E,” Applied Mathematics Letters, vol. 11, pp. 121-123, 1998.
  • Referans12 G. Adomian and R. Rach, “Linear and nonlinear Schröndinger equations,” in Foundations Of Physics, Kluwer Academic Publishers-Plenum, vol. 21, pp. 983-991, 1991.
  • Referans13 G. Adomian and R. Rach, “Inhomogeneous nonlinear partial differential equations with variable coefficients,” Applied Mathematics Letters, vol. 5, pp. 11-12, 1992.
  • Referans14 G. Adomian and R. Rach, “Modified decomposition solutions of nonlinear partial differential equations,” Applied Mathematics Letters, vol. 5, pp. 29-30, 1992.
  • Referans15 G.Adomian and R. Rach, “A modified decomposition series,” Computers And Mathematacis with Applications, vol. 23, pp. 17-23, 1992.
  • Referans16 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.
  • Referans17 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.
  • Referans18 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.
  • Referans19 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.
  • Referans20 K. Majid and M. Hussain, “Application of Laplace decomposition method on semi-infinite domain,” Numerical Algorithms., vol. 56, pp. 211-218, 2011.
  • Referans21 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.
  • Referans22 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.

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

Year 2017, Volume: 21 Issue: 6, 1524 - 1528, 01.12.2017

Hami Gündoğdu Ömer Faruk Gözükızıl

https://doi.org/10.16984/saufenbilder.340379

Abstract

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.

Keywords

laplace ayrışma Metodu Adomian ayrışma Metodu Benney-Luke denklemi parazit terimler

References

  • Referans1 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.
  • Referans2 G.-L. Liu, “New research directions in singular perturbation theory: artificial parameter approach and inverse-perturbation technique,” Proceeding of the 7th Conference of the Modern Mathematics and Mechanics, Shanghai, pp. 47-53, 1997.
  • Referans3 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.
  • Referans4 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.
  • Referans5 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.
  • Referans6 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.
  • Referans7 G. Adomian, “Nonlinear stochastic systems theory and applications to physics,” in Mathematics And Its Applications, Kluwer Academic Publishers, vol. 46 pp. 10-224, 1989.
  • Referans8 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.
  • Referans9 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.
  • Referans10 G. Adomian, “Solution of physical problems by decomposition,” Computers And Mathematacis with Applications, vol. 27, pp. 145-154, 1994.
  • Referans11 G. Adomian, “Solution of nonlinear P.D.E,” Applied Mathematics Letters, vol. 11, pp. 121-123, 1998.
  • Referans12 G. Adomian and R. Rach, “Linear and nonlinear Schröndinger equations,” in Foundations Of Physics, Kluwer Academic Publishers-Plenum, vol. 21, pp. 983-991, 1991.
  • Referans13 G. Adomian and R. Rach, “Inhomogeneous nonlinear partial differential equations with variable coefficients,” Applied Mathematics Letters, vol. 5, pp. 11-12, 1992.
  • Referans14 G. Adomian and R. Rach, “Modified decomposition solutions of nonlinear partial differential equations,” Applied Mathematics Letters, vol. 5, pp. 29-30, 1992.
  • Referans15 G.Adomian and R. Rach, “A modified decomposition series,” Computers And Mathematacis with Applications, vol. 23, pp. 17-23, 1992.
  • Referans16 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.
  • Referans17 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.
  • Referans18 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.
  • Referans19 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.
  • Referans20 K. Majid and M. Hussain, “Application of Laplace decomposition method on semi-infinite domain,” Numerical Algorithms., vol. 56, pp. 211-218, 2011.
  • Referans21 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.
  • Referans22 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.
There are 22 citations in total.

Details

Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Hami Gündoğdu

Ömer Faruk Gözükızıl

Publication Date December 1, 2017
Submission Date September 28, 2017
Acceptance Date October 17, 2017
Published in Issue Year 2017 Volume: 21 Issue: 6

Cite

APA Gündoğdu, H., & Gözükızıl, Ö. F. (2017). Obtaining the solution of Benney-Luke Equation by Laplace and adomian decomposition methods. Sakarya University Journal of Science, 21(6), 1524-1528. https://doi.org/10.16984/saufenbilder.340379
AMA Gündoğdu H, Gözükızıl ÖF. Obtaining the solution of Benney-Luke Equation by Laplace and adomian decomposition methods. SAUJS. December 2017;21(6):1524-1528. doi:10.16984/saufenbilder.340379
Chicago Gündoğdu, Hami, and Ömer Faruk Gözükızıl. “Obtaining the Solution of Benney-Luke Equation by Laplace and Adomian Decomposition Methods”. Sakarya University Journal of Science 21, no. 6 (December 2017): 1524-28. https://doi.org/10.16984/saufenbilder.340379.
EndNote Gündoğdu H, Gözükızıl ÖF (December 1, 2017) Obtaining the solution of Benney-Luke Equation by Laplace and adomian decomposition methods. Sakarya University Journal of Science 21 6 1524–1528.
IEEE H. Gündoğdu and Ö. F. Gözükızıl, “Obtaining the solution of Benney-Luke Equation by Laplace and adomian decomposition methods”, SAUJS, vol. 21, no. 6, pp. 1524–1528, 2017, doi: 10.16984/saufenbilder.340379.
ISNAD Gündoğdu, Hami - Gözükızıl, Ömer Faruk. “Obtaining the Solution of Benney-Luke Equation by Laplace and Adomian Decomposition Methods”. Sakarya University Journal of Science 21/6 (December 2017), 1524-1528. https://doi.org/10.16984/saufenbilder.340379.
JAMA Gündoğdu H, Gözükızıl ÖF. Obtaining the solution of Benney-Luke Equation by Laplace and adomian decomposition methods. SAUJS. 2017;21:1524–1528.
MLA Gündoğdu, Hami and Ömer Faruk Gözükızıl. “Obtaining the Solution of Benney-Luke Equation by Laplace and Adomian Decomposition Methods”. Sakarya University Journal of Science, vol. 21, no. 6, 2017, pp. 1524-8, doi:10.16984/saufenbilder.340379.
Vancouver Gündoğdu H, Gözükızıl ÖF. Obtaining the solution of Benney-Luke Equation by Laplace and adomian decomposition methods. SAUJS. 2017;21(6):1524-8.
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