A fourth order one step method for numerical solution of good Boussinesq
equation

Irk, Dursun; Kırlı, Emre

doi:10.3906/mat-2105-18

A fourth order one step method for numerical solution of good Boussinesq equation

Emre KIRLI, (İstanbul Bilgi Üniversitesi, Mühendislik ve Doğa Bilimleri Fakültesi, Matematik Bölümü, İstanbul, Türkiye)

Dursun IRK (Eskişehir Osmangazi Üniversitesi, Fen-Edebiyat Fakültesi, Matematik ve Bilgisayar Bilimleri Bölümü, Eskişehir, Türkiye)

Turkish Journal of Mathematics

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Yıl: 2021 Cilt: 45 Sayı: 5 Sayfa Aralığı: 2154 - 2170 Metin Dili: İngilizce DOI: 10.3906/mat-2105-18 İndeks Tarihi: 01-07-2022

A fourth order one step method for numerical solution of good Boussinesq equation

Öz:

In this paper, we investigate the numerical solution of ”good” Boussinesq equation by using the quartic B-spline Galerkin method for space discretization and the fourth order one-step method for time discretization.The proposed numerical scheme is analyzed for truncation error. Four test problems are studied. The accuracy and efficiency are measured by computing error norm L∞ and the order of convergence for the proposed method. The results of numerical experiments confirm that the proposed method has a higher accuracy

Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Mohebbi A, Asgari Z. Efficient numerical algorithms for the solution of “good” Boussinesq equation in water wave propagation. Computer Physics Communications 2011; 182: 2464-2470. doi: 10.1016/j.cpc.2011.07.004
[2] Manoranjan VS, Mitchell AR, Morris JL. Numerical solutions of the good Boussinesq equation. SIAM Journal on Scientific and Statistical Computing 1984; 5(4): 946-957. doi: 10.1137/0905065
[3] Ortega T, Sanz-Sema JM. Nonlinear stability and convergence of finite difference methods for the “good”Boussinesq equation. Numerische Mathematik 1990; 58: 215-229. doi: 10.1007/BF01385620
[4] Pani AK, Saranga H. Finite element Galerkin method for the “good” Boussinesq equation. Nonlinear Analysis: Theory, Methods and Applications 1997; 29: 937-956. doi: 10.1016/S0362-546X(96)00093-4
[5] El-Zoheiry H. Numerical investigation for the solitary waves interaction of the “good”Boussinesq equation. Applied Numerical Mathematics 2003; 45: 161-173. doi: 10.1016/S0168-9274(02)00187-3
[6] Wazwaz AM. Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method. Chaos, Solitons and Fractals 2001; 12: 549-1556. doi: 10.1016/S0960-0779(00)00133-8
[7] Ismail MS, Bratsos AG. A predictor- corrector scheme for the numerical solutions of the Boussinesq equation. Journal of Applied Mathematics and Computing 2003; 13: 11-27. doi: 10.1007/BF02936071
[8] Bratsos AG, Tsitouras Ch, Natsis DG. Linearized numerical schemes for the Boussinesq equation. Applied Numerical Analysis and Computational Mathematics 2005; 2: 34-53. doi: 10.1002/anac.200410021
[9] Bratsos AG. The solution of the Boussinesq equation using the method of lines. Computer Methods in Applied Mechanics and Engineering 1998; 157(1-2): 33-44. doi: 10.1016/S0045-7825(97)00211-9
[10] Bratsos AG. A second order numerical scheme for the solution of the one-dimensional Boussinesq equation. Numerical Algorithms 2007; 46: 45-58. doi: 10.1007/s11075-007-9126-y
[11] Bratsos AG. Solitary-wave propagation and interactions for the “good” Boussinesq equation. International Journal of Computer Mathematics 2008; 85: 1431-1440. doi: 10.1080/00207160701509740
[12] Al-Khaled K, Nusier AS. Numerical investigation for solitary solutions of the Boussinesq equation. Applied Mathematics E - Notes 2008; 8: 159-170
[13] Dehghan M, Salehi RA. Meshless based numerical technique for traveling solitary wave solution of Boussinesq equation. Applied Mathematical Modelling 2012; 36(5): 1939-1956. doi: 10.1016/j.apm.2011.07.075
[14] Siddiqi SS, Arshed S. Quintic B-spline for the numerical solution of the good Boussinesq equation. Journal of the Egyptian Mathematical Society 2014; 22(2): 209-213. doi: 10.1016/j.joems.2013.06.015
[15] Ismail MS, Mosally F. A fourth order finite difference method for the good Boussinesq equation. Abstract and Applied Analysis 2014; Article ID 323260, 10 pages. doi: 10.1155/2014/323260
[16] Ucar Y, Esen A, Karaagac B. Numerical solutions of Boussinesq equation using Galerkin finite element method. Numerical Methods for Partial Differential Equations 2020; 3782: 1612-1630. doi: 10.1002/num.22600

APA	Kırlı E, Irk D (2021). A fourth order one step method for numerical solution of good Boussinesq equation. , 2154 - 2170. 10.3906/mat-2105-18
Chicago	Kırlı Emre,Irk Dursun A fourth order one step method for numerical solution of good Boussinesq equation. (2021): 2154 - 2170. 10.3906/mat-2105-18
MLA	Kırlı Emre,Irk Dursun A fourth order one step method for numerical solution of good Boussinesq equation. , 2021, ss.2154 - 2170. 10.3906/mat-2105-18
AMA	Kırlı E,Irk D A fourth order one step method for numerical solution of good Boussinesq equation. . 2021; 2154 - 2170. 10.3906/mat-2105-18
Vancouver	Kırlı E,Irk D A fourth order one step method for numerical solution of good Boussinesq equation. . 2021; 2154 - 2170. 10.3906/mat-2105-18
IEEE	Kırlı E,Irk D "A fourth order one step method for numerical solution of good Boussinesq equation." , ss.2154 - 2170, 2021. 10.3906/mat-2105-18
ISNAD	Kırlı, Emre - Irk, Dursun. "A fourth order one step method for numerical solution of good Boussinesq equation". (2021), 2154-2170. https://doi.org/10.3906/mat-2105-18

APA	Kırlı E, Irk D (2021). A fourth order one step method for numerical solution of good Boussinesq equation. Turkish Journal of Mathematics, 45(5), 2154 - 2170. 10.3906/mat-2105-18
Chicago	Kırlı Emre,Irk Dursun A fourth order one step method for numerical solution of good Boussinesq equation. Turkish Journal of Mathematics 45, no.5 (2021): 2154 - 2170. 10.3906/mat-2105-18
MLA	Kırlı Emre,Irk Dursun A fourth order one step method for numerical solution of good Boussinesq equation. Turkish Journal of Mathematics, vol.45, no.5, 2021, ss.2154 - 2170. 10.3906/mat-2105-18
AMA	Kırlı E,Irk D A fourth order one step method for numerical solution of good Boussinesq equation. Turkish Journal of Mathematics. 2021; 45(5): 2154 - 2170. 10.3906/mat-2105-18
Vancouver	Kırlı E,Irk D A fourth order one step method for numerical solution of good Boussinesq equation. Turkish Journal of Mathematics. 2021; 45(5): 2154 - 2170. 10.3906/mat-2105-18
IEEE	Kırlı E,Irk D "A fourth order one step method for numerical solution of good Boussinesq equation." Turkish Journal of Mathematics, 45, ss.2154 - 2170, 2021. 10.3906/mat-2105-18
ISNAD	Kırlı, Emre - Irk, Dursun. "A fourth order one step method for numerical solution of good Boussinesq equation". Turkish Journal of Mathematics 45/5 (2021), 2154-2170. https://doi.org/10.3906/mat-2105-18