Solitary wave solutions of the MRLW equation using a spatial five-point stencil of finite difference approximation

Springer Science and Business Media LLC - 2023
Nouf Alotaibi1, Hasan Alzubaidi2
1Department of Mathematics, Faculty of Applied Sciences, Umm Al-Qura University, Makkah, Saudi Arabia
2Department of Mathematics, Al-Qunfudah University College, Umm Al-Qura University, Al-Qunfudah, Saudi Arabia

Tóm tắt

AbstractThis paper proposes a finite difference scheme with a three-level time and a five-point stencil in space to solve an initial boundary value problem for the MRLW equation. The scheme is shown to be marginally stable and convergent with a fourth-order convergence in the space direction and a second-order convergence in the time variable direction with regard to the maximum norm. The conservation properties of the proposed scheme are assessed using the three motion invariants for mass, momentum, and energy. To validate the theoretical results, numerical experiments are given for both single and interaction of two and three solitary waves.

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Tài liệu tham khảo

Drazin PC (1983) Solitons, 1st edn. Cambridge University Press, Cambridge

Peregrine DH (1966) Calculations of the development of an undular bore. J Fluid Mech 25:321–330

Benjamin TB, Bona JL, Mahony JJ (1972) Model equations for long waves in nonlinear dispersive systems. Philos Trans R Soc B Biol Sci 272:47–78

Eilbeck JC, McGuire GR (1975) Numerical study of RLW equation I: numerical methods. J Comput Phys 19:43–57

Zhang L (2005) A finite difference scheme for generalized long wave equation. Appl Math Comput 168:962–972

Khalifa AK, Raslan KR, Alzubaidi HM (2007) A finite difference scheme for the mrlw and solitary wave interactions. Appl Math Comput 189:346–354

Rouatbi A, Labidi M, Omrani K (2020) Conservative difference scheme of solitary wave solutions of the generalized regularized long-wave equation. Indian J Pure Appl Math 51:1317–1342

Bayarassou K, Rouatbi A, Omrani K (2020) Uniform error estimates of fourth-order conservative linearized difference scheme for a mathematical model for long wave. Int J Comput Math 97:678–1703

Ghiloufi A, Rouatbi A, Omrani K (2018) A new conservative fourth-order accurate difference scheme for solving a model of nonlinear dispersive equations. Math Methods Appl Sci 41:1–24

Dogan A (2002) Numerical solution of rlw equation using linear finite element within Galerkin method. Appl Math Model 26:771–783

Roshan T (2012) A petrov galerkin method for solving the generalized regularized long wave (grlw) equation. Comput Math Appl 63:943–956

Karakoc SBG, Mei L, Ali KK (2021) Two efficient methods for solving the generalized regularized long wave equation. Appl Anal 101:4721–4742

Karakoc SBG, Bhowmik SK (2019) Numerical approximation of the generalized regularized long wave equation using Petrov-Galerkin finite element method. Numer Methods Partial Differ Equ 35:2236–2257

Gao F, Qiao F, Rui H (2015) Numerical simulation of the modified regularized long wave equation by split least-squares mixed finite element method. Math Comput Simul 109:64–73

Gu H, Chen N (2008) Least squares mixed finite element methods for the rlw equations. Numer Methods Partial Differ Equ 24:749–758

Khalifa AK, Raslan KR, Alzubaidi HM (2008) A collocation method with cubic b-spline for solving the mrlw eqution. J Comput Appl Math 212:406–418

Raslan KR, Hassan SM (2009) Solitary waves for the mrlw equation. Appl Math Lett 22:984–989

Mohammed PO, Alqudah MA, Hamed YS, Kashuri A, Abualnaja KM (2021) Solving the modified regularized long wave equations via higher degree b-spline algorithm. J Funct Spaces 2021:1–10

Djidjeli K, Price WG, Twizell EH, Cao Q (2003) A linearized implicit pseudo-spectral method for some model equations: the regularized long wave equations. Int J Numer Methods Biomed Eng 19:847–863

Hammad DA, El-Azab MS (2016) Chebyshev-chebyshev spectral collocation method for solving the generalized regularized long wave (GRLW) equation. Appl Math Comput 285:228–240

El-Danaf TS, Ramadan MA, Alaal FEIA (2005) The use of adomian decomposition method for solving the regularized long-wave equation. Chaos Solit Fract 26:747–757

Khalifa AK, Raslan KR, Alzubaidi HM (2008) Numerical study using adm for the modified regularized long wave equation. Appl Math Model 32:2962–2972

Akbari R, Mokhtari R (2014) A new compact finite difference method for solving the generalized long wave equation. Numer Funct Anal Optim 35:133–152

Inan B, Bahadir AR (2015) Numerical solutions of mrlw equation by a fully implicit finite-difference scheme. J Math Comput Sci 15:228–239

Olver PJ (1979) Euler operators and conservation laws of the bbm equation. Math Proc Camb Philos Soc 85:143–159

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