Conservative compact difference scheme for the generalized Korteweg-de Vries equation

References

• T. Ak, S.B.G. Karakoc, and A. Biswas, Numerical scheme to dispersive shallow water waves, J. Comput. Theor. Nanosci. 13 (2016), pp. 7084–7092.
   Google Scholar
• T. Ak, S.B.G. Karakoc, and A. Biswas, A new approach for numerical solution of modified Korteweg-de Vries equation, Iran. J. Sci. Technol. Trans. Sci. 41 (2017), pp. 1109–1121.
   Web of Science ®Google Scholar
• A. Aydin and C. Koroglu, A nonstandard numerical method for the modified KdV equation, Pramana-J. Phys. 89 (2017), p. 72.
   Web of Science ®Google Scholar
• K. Bayarassou, A. Rouatbi, and K. Omrani, Uniform error estimates of fourth-order conservative linearized difference scheme for a mathematical model for long wave, Int. J. Comput. Math. 97 (2020), pp. 1678–1703.
   Web of Science ®Google Scholar
• A. Biswas and K.R. Raslan, Numerical simulation of the modified Korteweg-de Vries equation, Phys. Wave Phenom. 19 (2011), pp. 142–147.
   Web of Science ®Google Scholar
• H. Cheng and X. Wang, A high-order linearized difference scheme preserving dissipation property for the 2D Benjamin-Bona-Mahony-Burgers equation, J. Math. Anal. Appl. 500 (2021), Article ID 125182.
   Web of Science ®Google Scholar
• R. Chousurin, T. Mouktonglang, B. Wongsaijai, and K. Poochinapan, Performance of compact and non-compact structure preserving algorithms to traveling wave solutions modeled by the Kawahara equation, Numer. Algorithms 85 (2020), pp. 523–541.
   Web of Science ®Google Scholar
• Y. He, X. Wang, H. Cheng, and Y. Deng, Numerical analysis of a high-order accurate compact finite difference scheme for the SRLW equation, Appl. Math. Comput. 418 (2022), pp. 126837.
   Web of Science ®Google Scholar
• A. Ghiloufi and K. Omrani, New conservative difference schemes with fourth-order accuracy for some model equation for nonlinear dispersive waves, Numer. Methods Partial Differ. Equ. 34 (2018), pp. 451–500.
   Web of Science ®Google Scholar
• A. Ghiloufi, M. Rahmeni, and K. Omrani, Convergence of two conservative high-order accurate difference schemes for the generalized Rosenau-Kawahara-RLW equation, Eng. Comput. 36 (2020), pp. 617–632.
   Web of Science ®Google Scholar
• F.E. Ham, F.S. Lien, and A.B. Strong, A fully conservative second-order finite difference scheme for incompressible flow on nonuniform grids, J. Comput. Phys. 177 (2002), pp. 117–133.
   Web of Science ®Google Scholar
• D.D. He, New solitary solutions and a conservative numerical method for the Rosenau-Kawahara equation with power law nonlinearity, Nonlinear Dynam. 82 (2015), pp. 1177–1190.
   Web of Science ®Google Scholar
• D.D. He, Exact solitary solution and a three-level linearly implicit conservative finite difference method for the generalized Rosenau-Kawahara-RLW equation with generalized Novikov type perturbation, Nonlinear Dynam. 85 (2016), pp. 479–498.
   Web of Science ®Google Scholar
• D.D. He and K. Pan, A linearly implicit conservative difference scheme for the generalized Rosenau-Kawahara-RLW equation, Appl. Math. Comput. 271 (2015), pp. 323–336.
   Web of Science ®Google Scholar
• H.N.A. Ismail, K.R. Raslan, and G.S.E. Salem, Solitary wave solutions for the general KDV equation by Adomian decomposition method, Appl. Math. Comput. 154 (2004), pp. 17–29.
   Web of Science ®Google Scholar
• S.B.G. Karakoc, A quartic subdomain finite element method for the modified KdV equation, Stat. Optim. Inf. Comput. 6 (2018), pp. 609–618.
   Google Scholar
• S.B.G. Karakoc, Numerical solutions of the modified KdV equation with collocation method, Malaya J. Mat. 6 (2018), pp. 835–842.
   Google Scholar
• S.B.G. Karakoc and T. Ak, Numerical solution of Rosenau-KdV equation using subdomain finite element method, New Trends Math. Sci. 4 (2016), pp. 223–235.
   Google Scholar
• S.B.G. Karakoc and K.K. Ali, New exact solutions and numerical approximations of the generalized KdV equation, Comput. Methods Differ. Equ. 9 (2021), pp. 670–691.
   Web of Science ®Google Scholar
• S.B.G. Karakoc and H. Zeybek, Solitary-wave solutions of the GRLW equation using septic B-spline collocation method, Appl. Math. Comput. 289 (2016), pp. 159–171.
   Web of Science ®Google Scholar
• S.B.G. Karakoc, A. Saha, and D. Sucu, A novel implementation of Petrov-Galerkin method to shallow water solitary wave pattern and superperiodic traveling wave and its multistability: Generalized Korteweg-de Vries equation, Chinese J. Phys. 68 (2020), pp. 605–617.
   Web of Science ®Google Scholar
• D.J. Kortewe and G. de Vries, On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Lond. Edinb. Dublin Philos. Mag. J. Sci. 39 (1895), pp. 422–443.
   Google Scholar
• S. Nanta, S. Yimnet, K. Poochinapan, and B. Wongsaijai, On the identification of nonlinear terms in the generalized Camassa-Holm equation involving dual-power law nonlinearities, Appl. Numer. Math.160 (2021), pp. 386–421.
   Web of Science ®Google Scholar
• X.F. Wang and H. Cheng, Solitary wave solution and a linear mass-conservative difference scheme for the generalized Korteweg-de Vries-Kawahara equation, Comput. Appl. Math. 40 (2021), pp. 273.
   Web of Science ®Google Scholar
• X.F. Wang and W. Dai, A new implicit energy conservative difference scheme with fourth-order accuracy for the generalized Rosenau-Kawahara-RLW equation, Comput. Appl. Math. 37 (2018), pp. 6560–6581.
   Web of Science ®Google Scholar
• X.F. Wang and W. Dai, A conservative fourth-order stable finite difference scheme for the generalized Rosenau-KdV equation in both 1D and 2D, J. Comput. Appl. Math. 355 (2019), pp. 310–331.
   Web of Science ®Google Scholar
• X.F. Wang, H. Cheng, and W. Dai, Conservative and fourth-order compact diference schemes for the generalized Rosenau-Kawahara-RLW equation, Eng. Comput. 38 (2022), pp. 1491–1514.
   Web of Science ®Google Scholar
• X.F. Wang, W. Dai, and M. Usman, A high-order accurate finite difference scheme for the KdV equation with time-periodic boundary forcing, Appl. Numer. Math. 160 (2021), pp. 102–121.
   Web of Science ®Google Scholar
• A.-M. Wazwaz, Variants of the generalized KdV equation with compact and noncompact structures, Comput. Appl. Math. 47 (2004), pp. 583–591.
   Web of Science ®Google Scholar
• B. Wongsaijai, K. Poochinapan, and T. Disyadej, A compact finite difference method for solving the General Rosenau-RLW equation, Int. J. Appl. Math. 44 (2014), pp. 192–199.
   Google Scholar
• B. Wongsaijai, T. Mouktonglang, N. Sukantamala, and K. Poochinapan, Compact structure-preserving approach to solitary wave in shallow water modeled by the Rosenau-RLW equation, Appl. Math. Comput. 340 (2019), pp. 84–100.
   Web of Science ®Google Scholar
• Y. Zhou, Application of Discrete Functional Analysis to the Finite Difference Method, Inter. Acad. Publishers, Beijing, 1991.
   Google Scholar