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Numerical Algorithms
Published in: Numerical Algorithms 2/2020

25-05-2020 | Original Paper

Performance of compact and non-compact structure preserving algorithms to traveling wave solutions modeled by the Kawahara equation

Authors: R. Chousurin, T. Mouktonglang, B. Wongsaijai, K. Poochinapan

Published in: Numerical Algorithms | Issue 2/2020

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Abstract

The main contribution of this article is to introduce new compact fourth-order, standard fourth-order, and standard second-order finite difference schemes for solving the Kawahara equation, the fifth-order partial derivative equation. The conservation of mass only of the numerical solution obtained by the compact fourth-order finite difference scheme is proven. However, the standard fourth-order and standard second-order finite difference schemes can preserve both mass and energy. The stability is also proven by von Neumann analysis. According to analysis for numerical experiments, the order of accuracy for each scheme and the computational efficiency of the compact scheme are presented. To validate the potential of the presented methods, we also consider long-time behavior. Finally, results obtained from the compact scheme are superior than those from the non-compact schemes.
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Literature
1.
Kakutani, T., Ono, H.: Weak non-linear hydromagnetic waves in a cold collision-free plasma. J. Phys. Soc. Japan. 26(5), 1305–1318 (1969)CrossRef
2.
Hasimoto, H.: Water waves. Kagaku 40, 401–408 (1970)
3.
Iguchi, T.: A long wave approximation for capillary-gravity waves and the Kawahara equation. Bull. Inst. Math. Acad. Sin. (N.S.) 2, 179–220 (2007)MathSciNetMATH
4.
Kawahara, T.: Oscillatory solitary waves in dispersive media. Phys. Soc. Japan. 33(1), 260–264 (1972)CrossRef
5.
Shukla, R.K., Tatineni, M., Zhong, X.: Very high-order compact finite difference schemes on non-uniform grids for incompressible Navier-Stokes equations. J. Comput. Phys. 224, 1064–1094 (2007)MathSciNetMATHCrossRef
6.
Shah, A., Yuan, L., Khan, A.: Upwind compact finite difference scheme for time-accurate solution of the incompressible Navier-Stokes equations. Appl. Math. Comput. 215, 3201–3213 (2010)MathSciNetMATH
7.
Wongsaijai, B., Poochinapan, K., Disyadej, T.: A compact finite difference method for solving the general Rosenau-RLW equation. IAENG Int. J. Appl. Math. 44(4), 192–199 (2014)MathSciNetMATH
8.
Miyatake, Y., Matsuo, T.: Conservative finite difference schemes for the Degasperis-Procesi equation. J. Comput. Appl. Math. 236(15), 3728–3740 (2012)MathSciNetMATHCrossRef
9.
Miyatake, Y., Matsuo, T.: Energy-preserving H1-Galerkin schemes for shallow water wave equations with peakon solutions. Phys. Lett. A 376, 2633–2639 (2012)MathSciNetMATHCrossRef
10.
Poochinapan, K., Wongsaijai, B., Disyadej, T.: Efficiency of high-order accurate difference schemes for the Korteweg-de Vries equation. Math. Probl. Eng 2014(862403), 8 (2014)MathSciNetMATH
11.
12.
Ezzati, R., Shakibi, K., Ghasemimanesh, M.: Using multiquadric quasi-interpolation for solving Kawahara equation. Int. J. Industrial Math. 3(2), 111–123 (2011)
13.
Bibi, N., Tirmizi, S.I.A., Haq, S.: Meshless method of lines for numerical solution of Kawahara type equations. Appl. Math. 2, 608–618 (2011)MathSciNetCrossRef
14.
Suarez, P.U., Morales, J.H.: Fourier splitting method for Kawahara type equation. J. Comput. Methods in Phys. 2014(894956), 4 (2014)MATH
15.
Karakoc, B.G., Zeybek, H., AK, T.: Numerical solutions of the Kawahara equation by the septic B-spline collocation method. Stat. Optim. Inf. Comput. 2, 211–221 (2014)MathSciNetMATHCrossRef
16.
Korkmaz, A., Dag, I.: Crank-Nicolson-differential quadrature algorithms for the Kawahara equation. Chaos Solitons Fractals 42, 64–73 (2009)MathSciNetMATHCrossRef
17.
Bashan, A.: An efficient approximation to numerical solutions for the Kawahara equation via modified cubic B-spline differntial quadrature method. Mediterr. J. Math 16(14) (2019)
18.
Sepulveda, M., Villagran, O.P.V.: Numerical method for a transport equation perturbed by dispersive terms of 3rd and 5nd order. Sci. Ser. A Math. Sci. (N.S.) 13, 13–21 (2006)MathSciNetMATH
19.
Ceballos, J., Sepulveda, M., Villagran, O.P.V.: The Korteweg de Vries Kawahara equation in a boundary domain and numerical results. Appl. Math. Comput. 190(2), 912–936 (2007)MathSciNetMATH
20.
Koley, U.: Finite difference schemes for the Korteweg-de vries-Kawahara equation. Int. J. Numer. Anal. Model. 13(3), 344–367 (2015)MathSciNetMATH
21.
Omrani, K., Abidi, F., Achouri, T., Khiari, N.: A new conservative finite difference scheme for the Rosenau equation. Appl. Math. Comput. 201, 35–43 (2008)MathSciNetMATH
22.
Pan, X., Zhang, L.: A new finite difference scheme for the Rosenau-Burgers equation. Appl. Math. Comput. 218, 8917–8924 (2012)MathSciNetMATH
23.
Pan, X., Zhang, L.: On the convergence of a conservative numerical scheme for the usual Rosenau-RLW equation. Appl. Math. Model. 36, 3371–3378 (2012)MathSciNetMATHCrossRef
24.
Wongsaijai, B., Poochinapan, K.: A three-level average implicit finite difference scheme to solve equation obtainded by coupling the Rosenau-KdV equation and the Rosenau-RLW equation. Appl. Math. Comput. 245, 289–304 (2014)MathSciNetMATH
25.
He, D., Pan, K.: A linearly implicit conservative difference scheme for the generalized Rosenau-Kawahara-RLW equation. Appl. Math. Comput. 271, 323–336 (2015)MathSciNetMATH
26.
He, D.: 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, 479–498 (2016)MathSciNetMATHCrossRef
27.
Metadata
Title
Performance of compact and non-compact structure preserving algorithms to traveling wave solutions modeled by the Kawahara equation
Authors
R. Chousurin
T. Mouktonglang
B. Wongsaijai
K. Poochinapan
Publication date
25-05-2020
Publisher
Springer US
Published in
Numerical Algorithms / Issue 2/2020
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-019-00825-4

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