دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات44
تعداد شماره‌ها1,303
تعداد مقالات16,020
تعداد مشاهده مقاله52,486,847
تعداد دریافت فایل اصل مقاله15,213,889
Karta, Melike. (1403). A new perspective for the Quintic B-spline collocation method via the Lie-Trotter splitting algorithm to solitary wave solutions of the GEW equation. سامانه مدیریت نشریات علمی, 12(3), 544-560. doi: 10.22034/cmde.2024.58169.2454
Melike Karta. "A new perspective for the Quintic B-spline collocation method via the Lie-Trotter splitting algorithm to solitary wave solutions of the GEW equation". سامانه مدیریت نشریات علمی, 12, 3, 1403, 544-560. doi: 10.22034/cmde.2024.58169.2454
Karta, Melike. (1403). 'A new perspective for the Quintic B-spline collocation method via the Lie-Trotter splitting algorithm to solitary wave solutions of the GEW equation', سامانه مدیریت نشریات علمی, 12(3), pp. 544-560. doi: 10.22034/cmde.2024.58169.2454
Karta, Melike. A new perspective for the Quintic B-spline collocation method via the Lie-Trotter splitting algorithm to solitary wave solutions of the GEW equation. سامانه مدیریت نشریات علمی, 1403; 12(3): 544-560. doi: 10.22034/cmde.2024.58169.2454

A new perspective for the Quintic B-spline collocation method via the Lie-Trotter splitting algorithm to solitary wave solutions of the GEW equation

Computational Methods for Differential Equations
مقاله 9، دوره 12، شماره 3، مهر 2024، صفحه 544-560    اصل مقاله (455.26 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.58169.2454
نویسنده
Melike Karta*
Department of Mathematics, Faculty of Science and Arts, Ağrı İbrahim Çeçen University, Ağrı, Turkey.
چکیده
A hybrid method utilizing the collocation technique with B-splines and Lie-Trotter splitting algorithm applied for 3 model problems which include a single solitary wave,  two solitary wave interaction, and a Maxwellian initial condition is designed for getting the approximate solutions for the generalized equal width (GEW) equation. Initially, the considered problem has been split into 2 sub-equations as linear $U_t=\hat{A}(U)$ and nonlinear $U_t=\hat{B}(U)$ in the  terms of time.  After, numerical schemes have been constructed for these sub-equations utilizing the finite element method (FEM) together with quintic B-splines. Lie-Trotter splitting technique $\hat{A}o\hat{B}$ has been  used to generate approximate solutions of the main equation. The stability analysis of acquired numerical schemes has been examined by the Von Neumann method. Also, the error norms $L_2$ and $L_\infty$ with mass, energy, and momentum conservation constants $I_1$, $I_2$, and $I_3$, respectively are calculated to illustrate how perfect solutions this new algorithm applied to the problem generates and the ones produced are compared with those in the literature. These new results exhibit that the algorithm presented in this paper is more accurate and successful, and easily applicable to other non-linear partial differential equations (PDEs) as the present equation.
کلیدواژه‌ها
B-splines؛ Lie-Trotter splitting؛ Collocation method؛ Generalized equal width equation
مراجع
  • [1] M. Abbaszadeh, M. Bayat, and M. Dehghan, The local meshless collocation method for numerical simulation of shallow water waves based on generalized equal width (GEW) equation, Wave Motion, 107 (2021), 102805.
  • [2] A. Babu and N. Asharaf, Numerical solution of nonlinear Sine-Gordon equation using modified cubic Bspline-based differential quadrature method, Computational Methods for Differential Equations, 11(2) (2023), 369-386.
  • [3] M. A. Banaja and H. O. Bakodah, Runge-Kutta integration of the equal width wave equation using the method of lines, Math. Probl. Eng., (2015), 1-9.
  • [4] A. Ba¸shan, N. M. Ya˘gmurlu, Y. Uc¸ar, and A. Esen, Finite difference method combined with differential quadrature method for numerical computation of the modified equal width wave equation, Numer. Methods Partial Differ. Equations., 37 (2009), 690-706.
  • [5] A. Ba¸shan, Single Solitary Wave and Wave Generation Solutions of the Regularised Long Wave (RLW) Equation, G.U. J. Sci, 35(4) (2022), 1597-1612.
  • [6] A. Ba¸shan, A novel outlook to the an alternative equation for modelling shallow water wave: Regularised Long Wave (RLW) equation,Indian J. Pure Appl. Math., (2022).
  • [7] A. Ba¸shan and N. M. Ya˘gmurlu, A mixed method approach to the solitary wave, undular bore and boundary-forced solutions of the Regularized Long Wave equation, Computational and Applied Mathematics, 41(169) (2022),
  • [8] T. B. Benjamin, J. L Bona, and J. J Mahony, Model equations for long waves in non-linear dispersive systems,Philosophical Transactions of the Royal Society of London Series A, 272 (1972), 47–78.
  • [9] S. K. Bhowmik and S. B. G. Karakoc, Numerical solutions of the generalized equal width wave equation using the Petrov–Galerkin method, Applicable Analysis , 100(4) (2021), 714–73.
  • [10] F. Bulut, O. Oru¸c, and A. Esen,¨ Higher order Haar wavelet method integrated with strang splitting for solving regularized long wave equation , Mathematics and Computers in Simulation, 197 (2022), 277–290.
  • [11] I. Da˘g, B. Saka, and D. Irk,˙ Galerkin method for the numerical solution of the RLW equation using quintic B-splines, Journal of Computational and Applied Mathematics, 190 (2006),532–547.
  • [12] A. Do˘gan, Application of Galerkin’s method to equal width wave equation, Applied Mathematics and Computation, 160 (2005), 65–76.
  • [13] A. Ebrahimijahan, M. Dehghan, and M. Abbaszadeh, Numerical simulation of shallow water waves based on generalized equal width (GEW) equation by compact local integrated radial basis function method combined with adaptive residual subsampling technique , Nonlinear Dyn., 105 (2021), 3359–3391.
  • [14] A. Esen, A numerical solution of the equal width wave equation by a lumped Galerkin method, Applied Mathematics and Computation, 168(1) (2005), 270–282.
  • [15] A. Esen, A lumped Galerkin method for the numerical solution of the modified equal-width wave equation using quadratic B-splines , Int. J. Comput. Math., 83(5-6) (2006), 449–459.
  • [16] A. Esen and S. Kutluay, Solitary wave solutions of the modified equal width wave equation, Commun. Non linear Sci. Numer. Simul., 13(3) (2008), 1538–1546.
  • [17] D. J. Evans and K. R. Raslan, Solitary waves for the generalized equal width (GEW) equation , International Journal of Computer Mathematics, 82(4) (2005), 445–455.
  • [18] L. R. T. Gardner and G. A. Gardner, Solitary waves of the equal width wave equation, Journal of Computational Physics, 101(1) (1991), 218–223.
  • [19] L. R. T. Gardner, G. A. Gardner, F. A. Ayoup, and N. K. Amein, Simulations of the EW undular bore, Commun. Numer. Meth. En., 13(7) (1997),583–592.
  • [20] L. R. T. Gardner, G. A. Gardner, and I. Da˘g, A B-spline finite element method for the regularized long wave equation, Commun. Numer. Methods Eng., 11 (1995), 59–68.
  • [21] J. Geiser, Iterative splitting methods for differential equations, in Numerical Analysis and Scientific Computing,Chapman and Hall/CRC, Boca Raton London New York, 2011.
  • [22] T. Geyikli and S. B. G. Karako¸c, Petrov–Galerkin method with cubic B-splines for solving the MEW equation , Bull. Belg. Math. Soc., Simon Stevin, 19 (2012), 215–227.
  • [23] H. Gu¨nerhan, M. Kaabar, and E. C¸elik, Novel analytical and approximate-analytical methods for solving the nonlinear fractional smoking mathematical model, Sigma J Eng Nat Sci, 41(2) (2023),331-343
  • [24] S. Hamdi, W. H. Enright, W. E. Schiesser, J. J. Gottlieb, and A. Alaal, Exact solutions of the generalized equal width wave equation, in : Proceedings of the International Conference on Computational Science and Its Applications, LNCS, 2668 (2003),725–734.
  • [25] R. Hedli and F. Berrimi, Novel Traveling Wave Solutions of Generalized Seventh-Order KdV Equation and Related Equation, Computational Methods for Differential Equations, 12(2) (2024), 392-412.
  • [26] W. Hundsdorfer and J. Verwer, Numerical solution of time-dependent advection-diffusion-reaction equations in Springer Series in Computational Mathematics, Springer, Verlag Berlin Heidelberg, 2003.
  • [27] B. Inan and A. R. Bahadir,˙ A Fully Implicit Finite Difference Approach for Numerical Solution of the Generalized Equal Width (GEW) Equation, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., 90(2) (2020),299–308.
  • [28] S. B. G. Karako¸c and H. Zeybek, A cubic B-spline Galerkin approach for the numerical simulation of the GEW equation, Stat. Optim. Inf. Comput., 4 (2016) 30–41.
  • [29] S. B. G. Karako¸c, K. Omrani, and D. Sucu, Numerical investigations of shallow water waves via generalized equal width (GEW) equation, Applied Numerical Mathematics, 162 (2021),249–264.
  • [30] S. B. G. Karakoc¸ and K. K. Ali, Analytical and computational approaches on solitary wave solutions of the generalized equal width equation, Applied Mathematics and Computation, 371 (2020), 124933.
  • [31] S. B. G. Karako¸c and H. Zeybek, A septic B-spline collocation method for solving the generalized equal width wave equation , Kuwait J. Sci., 43(3) (2016), 20-31.
  • [32] S. B. G. Karakoc¸, A numerical analysing of the GEW equation using finite element method, Journal of Science and Arts, 2(47) (2019) 339-348.
  • [33] S. B. G. Karako¸c and T. Geyikli, Numerical solution of the modified equal width wave equation, Int. J. Diff.Equations., (2012), 1–15.
  • [34] S. B. G. Karako¸c and T. Geyikli, A numerical solution of the MEW equation using sextic B-splines , J. Adv. Res. Appl. Math., 5(2013), 51–65.
  • [35] M. Karta, Two Effective Numerical Approaches for Equal Width Wave (EW) Equation Using Lie- Trotter Splitting Technique ,Konuralp Journal of Mathematics, 10(2) (2022), 220-232.
  • [36] M. Karta, A new application for numerical computations of the modified equal width equation (MEW) based on Lumped Galerkin method with the cubic B-spline ,Computational Methods for Differential Equations, 11(1) 2023, 95-107.
  • [37] S. Kutluay and A. Esen, A finite difference solution of the regularized long wave equation, Mathematical Problems in Engineering, 2006.
  • [38] M. Lakestani, Numerical Solutions of the KdV Equation Using B-Spline Functions, Iran J Sci Technol Trans Sci., 41 (2017), 409–417.
  • [39] G. I. Marchuk, Some application of splitting-up methods to the solution of mathematical physics problems , Aplikace matematiky, 13 (1968), 103–132.
  • [40] P. J. Morrison, J. D. Meiss, and J. R. Carey, Scattering of RLW solitary waves, Physica D, 11 ( 1984), 324–336.
  • [41] H. Panahipour, Numerical simulation of GEW equation using RBF collocation method, Communications in Numerical Analysis, 2012 (2012), 1–28.
  • [42] D. H. Peregrine, Long waves on a beach, Journal of Fluid Mechanics, 27(4) ( 1967), 815–827.
  • [43] P. M. Prenter, Splines and variational methods, J. Wiley, New York, 1975.
  • [44] K. R. Raslan, Collocation method using cubic B-spline for the generalised equal width equation , Int. J. Simulation and Process Modelling, 2 (2006), 37–44.
  • [45] K. R. Raslan, M. A. Ramadan, and I. G.Amıen, Finite difference approximations for the modified equal width wave (MEW) equation, J. Math Comput Sci., 4(5) (2014), 940-957.
  • [46] T. A. Roshan, Petrov-Galerkin method for solving the generalized equal width (GEW) equation, Journal of Computational and Applied Mathematics, 235(2011), 1641–1652.
  • [47] B. Saka, A finite element method for equal width equation, Applied Mathematics and Computation, 175(1) (2006),730–747.
  • [48] B. Sportisse, An analysis of operator splitting techniques in the stiff case , J. Comput. Phys. 161(2000), 140–168.
  • [49] N. Taghizadeh, M. Mirzazadeh, M. Akbari, and M. Rahimian, Exact solutions for generalized equal width equation, Math. Sci. Lett. 22, (2013) 99–106.
  • [50] N. M. Ya˘gmurlu and A. S. Karaka¸s, Numerical Solutions of the EW Equation By Trigonometric Cubic B-spline Collocation Method Based on Rubin-Graves Type Linearization, Numerical Methods for Partial Differential Equations, 36(5) (2020), 1170-1183.
  • [51] N. M. Ya˘gmurlu and A. S. Karaka¸s, A novel perspective for simulations of the MEW equation by trigonometric cubic B-spline collocation method based on Rubin-Graves type linearization, Computational Methods for Differential Equations.,(2021), 1-14.
  • [52] H. Zeybek and S. B. G. Karakoc, Application of the collocation method with B-splines to the GEW equation ,Electronic Transactions on Numerical Analysis, 46 (2017) 71–88.
آمار
تعداد مشاهده مقاله: 124
تعداد دریافت فایل اصل مقاله: 308


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب