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Applicable Analysis
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Volume 100, 2021 - Issue 4
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Articles

Numerical solutions of the generalized equal width wave equation using the Petrov–Galerkin method

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Pages 714-734 | Received 20 Feb 2019, Accepted 03 May 2019, Published online: 20 May 2019

References

  • Li Q, Mei L. Local momentum-preserving algorithms for the GRLW equation. Appl Math Comput. 2018;330:77–92.
  • Peregrine DH. Calculations of the development of an undular bore. J Fluid Mech. 1996;25:321–330.
  • Peregrine DH. Long waves on a beach. J Fluid Mech. 1967;27:815–827.
  • Benjamin TB, Bona JL, Mahony JJ. Model equations for waves in nonlinear dispersive systems. Philos Trans R Soc London. 1972;227:47–78.
  • Raslan KR, EL-Danaf TS, Ali KK. New numerical treatment for solving the KDV equation. J Abstr Comput Math. 2017;2(1):1–12.
  • Morrison PJ, Meiss JD, Carey JR. Scattering of RLW solitary waves. Physica. 1981;11D:324–336.
  • Hamdi S, Enright WH, Schiesser WE, et al. Exact solutions of the generalized equal width wave equation. Proceedings of the International Conference on Computational Science and Its Applications 2003;2668:725–734.
  • Karakoc SBG, Zeybek H. A cubic B-spline Galerkin approach for the numerical simulation of the GEW equation. Stat Optim Inf Comput. 2016;4:30–41.
  • Kaya D. A numerical simulation of solitary-wave solutions of the generalized regularized long wave equation. Appl Math Comput. 2004;149:833–841.
  • Kaya D, El-Sayed SM. An application of the decomposition method for the generalized KdV and RLW equations. Chaos Solitons Fractals. 2003;17:869–877.
  • Gardner LRT, Gardner GA, Geyikli T. The boundary forced MKdV equation. J Comput Phys. 1994;11:5–12.
  • Dodd RK, Eilbeck JC, Gibbon JD, et al. Solitons and nonlinear wave equations. New York (NY): Academic Press; 1982.
  • Lewis JC, Tjon JA. Resonant production of solitons in the RLW equation. Phys Lett A. 1979;73:275–279.
  • Panahipour H. Numerical simulation of GEW equation using RBF collocation method. Commun Numer Anal. 2012;2012:28 pages, doi:10.5899/2012/cna-00059
  • Gardner LRT, Gardner GA. Solitary waves of the equal width wave equation. J Comput Phys. 1991;101(1):218–223.
  • Gardner LRT, Gardner GA, Ayoup FA, et al. Simulations of the EW undular bore. Commun Numer Methods Eng. 1997;13:583–592.
  • Zaki SI. A least-squares finite element scheme for the EW equation. Comput Methods Appl Mech Eng. 2000;189(2):587–594.
  • Esen A. A numerical solution of the equal width wave equation by a lumped Galerkin method. Appl Math Comput. 2005;168(1):270–282.
  • Saka B. A finite element method for equal width equation. Appl Math Comput. 2006;175(1):730–747.
  • Dag I, Saka B. A cubic B-spline collocation method for the EW equation. Math Comput Appl. 2004;9(3):381–392.
  • Karakoc SBGK, Geyikli T. Numerical solution of the modified equal width wave equation. Int J Differ Equations. 2012;2012:1–15.
  • Geyikli T, Karakoc SBG. Petrov-Galerkin method with cubic B-splines for solving the MEW equation. Bull Belg Math Soc Simon Stevin. 2012;19:215–227.
  • Geyikli T, Karakoc SBG. Septic B-spline collocation method for the numerical solution of the modified equal width wave equation. Appl Math. 2011;2:739–749.
  • Geyikli T, Karakoc SBG. Subdomain finite element method with quartic B-splines for the modified equal width wave equation. Comput Math Math Phys. 2015;55(3):410–421.
  • Karakoc SBG. Numerical solutions of the modified equal width wave equation with finite elements method [PhD thesis]. Malatya: Inonu University; 2011.
  • Esen A. A lumped Galerkin method for the numerical solution of the modified equal-width wave equation using quadratic B-splines. Int J Comput Math. 2006;83(5–6):449–459.
  • Saka B. Algorithms for numerical solution of the modified equal width wave equation using collocation method. Math Comput Model. 2007;45(9–10):1096–1117.
  • Evans DJ, Raslan KR. Solitary waves for the generalized equal width (GEW) equation. Int J Comput Math. 2005;82(4):445–455.
  • Raslan KR. Collocation method using cubic B-spline for the generalised equal width equation. Int J Simul Process Modelling. 2006;2:37–44.
  • Taghizadeh N, Mirzazadeh M, Akbari M, et al. Exact solutions for generalized equal width equation. Math Sci Lett. 2013;2:99–106.
  • Zeybek H, Karakoc SBG. Application of the collocation method with B-splines to the GEW equation. Electron Trans Numer Anal. 2017;46:71–88.
  • Roshan T. A Petrov–Galerkin method for solving the generalized regularized equal width (GEW) equation. J Comput Appl Math. 2011;235:1641–1652
  • Atouani N, Omrani K. Galerkin finite element method for the Rosenau-RLW equation. Comput Math Appl. 2013;66(3):289–303
  • Thomee V. Galerkin finite element methods for parabolic problems. 2nd ed; Berlin: Springer; 2006. ISSN: 0179-3632. (Springer Series in Computational Mathematics.)
  • Ciarlet PG. The finite element method for elliptic problems. Paris: Society for Industrial and Applied Mathematics; 2002.
  • Karakoc SBG, Bhowmik SK. Galerkin finite element solution for Benjamin-Bona-Mahony-Burgers equation with cubic B-splines. Comput Math Appl. 2019;77(7):1917–1932.
  • Prenter PM. Splines and variational methods. New York (NY): John Wiley & Sons; 1975.

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