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Original Articles

A lumped Galerkin method for the numerical solution of the modified equal-width wave equation using quadratic B-splines

Pages 449-459 | Received 01 Aug 2005, Accepted 23 Jun 2006, Published online: 28 Nov 2010

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Ali Başhan, Yusuf Uçar, N. Murat Yağmurlu & Alaattin Esen. (2022) Numerical approximation to the MEW equation for the single solitary wave and different types of interactions of the solitary waves. Journal of Difference Equations and Applications 28:9, pages 1193-1213.
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Samir Kumar Bhowmik & Seydi Battal Gazi Karakoc. (2021) Numerical solutions of the generalized equal width wave equation using the Petrov–Galerkin method. Applicable Analysis 100:4, pages 714-734.
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Yılmaz Dereli. (2010) Radial basis functions method for numerical solution of the modified equal width equation. International Journal of Computer Mathematics 87:7, pages 1569-1577.
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Articles from other publishers (32)

Melike Karta. (2023) A numerical algorithm for solitary wave solutions of the GEW equation. Afrika Matematika 34:4.
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Raghda A.M. Attia, Youbing Xia, Xiao Zhang & Mostafa M.A. Khater. (2023) Exploring the dynamics of soliton waves: A comparative analysis of analytical and numerical methods for the modified Equal-Width equation. Results in Physics 50, pages 106578.
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Akeel A. AL-saedi & Jalil Rashidinia. (2023) Numerical Approximation of a Time-Fractional Modified Equal-Width Wave Model by Using the B-Spline Weighted Residual Method. Symmetry 15:4, pages 891.
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Chen Yue, M. Higazy, Omnia M. A. Khater & Mostafa M. A. Khater. (2023) Computational and numerical simulations of the wave propagation in nonlinear media with dispersion processes. AIP Advances 13:3.
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Minzhi Wei & Liping He. (2023) Existence of periodic wave for a perturbed MEW equation. AIMS Mathematics 8:5, pages 11557-11571.
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Seydi Battal Gazi KARAKOÇ, Derya SUCU & Mohamad Arif TAGHACHİ. (2022) NUMERICAL SIMULATION OF GENERALIZED OSKOLKOV EQUATION VIA THE SEPTIC B-SPLINE COLLOCATION METHOD. Journal of Universal Mathematics 5:2, pages 108-116.
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Rehana Ashraf, Saima Rashid, Fahd Jarad & Ali Althobaiti. (2022) Numerical solutions of fuzzy equal width models via generalized fuzzy fractional derivative operators. AIMS Mathematics 7:2, pages 2695-2728.
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Mostafa Abbaszadeh, Mostafa Bayat & Mehdi Dehghan. (2021) The local meshless collocation method for numerical simulation of shallow water waves based on generalized equal width (GEW) equation. Wave Motion 107, pages 102805.
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Ali Ebrahimijahan, Mehdi Dehghan & Mostafa Abbaszadeh. (2021) 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 Dynamics 105:4, pages 3359-3391.
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Ali Başhan, Nuri Murat Yağmurlu, Yusuf Uçar & Alaattin Esen. (2021) A new perspective for the numerical solution of the Modified Equal Width wave equation. Mathematical Methods in the Applied Sciences 44:11, pages 8925-8939.
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Liping He, Yuanhua Lin & Hongying Zhu. (2021) Some Smooth and Nonsmooth Traveling Wave Solutions for KP-MEW(2, 2) Equation. Journal of Mathematics 2021, pages 1-9.
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Seydi Battal Gazi Karakoc, Khaled Omrani & Derya Sucu. (2021) Numerical investigations of shallow water waves via generalized equal width (GEW) equation. Applied Numerical Mathematics 162, pages 249-264.
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Ömer Oruç. (2021) Delta-shaped basis functions-pseudospectral method for numerical investigation of nonlinear generalized equal width equation in shallow water waves. Wave Motion 101, pages 102687.
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Mobeen Munir, Muhammad Athar, Sakhi Sarwar & Wasfi Shatanawi. (2021) Lie symmetries of Generalized Equal Width wave equations. AIMS Mathematics 6:11, pages 12148-12165.
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Ali Başhan, N. Murat Yağmurlu, Yusuf Uçar & Alaattin Esen. (2020) Finite difference method combined with differential quadrature method for numerical computation of the modified equal width wave equation. Numerical Methods for Partial Differential Equations 37:1, pages 690-706.
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Bilge Inan & Ahmet Refik Bahadir. (2019) A Fully Implicit Finite Difference Approach for Numerical Solution of the Generalized Equal Width (GEW) Equation. Proceedings of the National Academy of Sciences, India Section A: Physical Sciences 90:2, pages 299-308.
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Seydi Battal GaziKarakoc & Khalid K. Ali. (2020) Analytical and computational approaches on solitary wave solutions of the generalized equal width equation. Applied Mathematics and Computation 371, pages 124933.
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Nuri Murat Yagmurlu, Berat Karaagac & Alaattin Esen. (2019) A Lumped Galerkin finite element method for the generalized Hirota-Satsuma coupled KdV and coupled MKdV equations. Tbilisi Mathematical Journal 12:3.
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İhsan Çelikkaya. (2019) Operator splitting method for numerical solution of modified equal width equation. Tbilisi Mathematical Journal 12:3.
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M.S. Hashemi, A. Haji-Badali, F. Alizadeh & D. Baleanu. (2017) Integrability, invariant and soliton solutions of generalized Kadomtsev-Petviashvili-modified equal width equation. Optik 139, pages 20-30.
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Ayşe Gül Kaplan & Yılmaz Dereli. (2017) Numerical solutions of the GEW equation using MLS collocation method. International Journal of Modern Physics C 28:01, pages 1750011.
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Halil Zeybek & S. Battal Gazi Karakoç. (2016) A numerical investigation of the GRLW equation using lumped Galerkin approach with cubic B-spline. SpringerPlus 5:1.
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Hany N. Hassan. (2016) An Accurate Numerical Solution for the Modified Equal Width Wave Equation Using the Fourier Pseudo-Spectral Method. Journal of Applied Mathematics and Physics 04:06, pages 1054-1067.
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Yasser M. Abo Essa. (2016) Multigrid Method for the Numerical Solution of the Modified Equal Width Wave Equation. Applied Mathematics 07:10, pages 1140-1147.
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T. Geyikli & S. B. G. Karakoc. (2015) Subdomain finite element method with quartic B-splines for the modified equal width wave equation. Computational Mathematics and Mathematical Physics 55:3, pages 410-421.
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Liyan Zhong, Shengqiang Tang, Dong Li & Haixia Zhao. (2014) Compacton, peakon, cuspons, loop solutions and smooth solitons for the generalized KP–MEW equation. Computers & Mathematics with Applications 68:12, pages 1775-1786.
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Shaoyong Li & Ming Song. (2014) Compacton-like wave and kink-like wave solutions of the generalized KP-MEW (2, 2) equation. Physica Scripta 89:3, pages 035202.
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R.J. Cheng & K.M. Liew. (2012) Analyzing modified equal width (MEW) wave equation using the improved element-free Galerkin method. Engineering Analysis with Boundary Elements 36:9, pages 1322-1330.
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Asit Saha. (2012) Bifurcation of travelling wave solutions for the generalized KP-MEW equations. Communications in Nonlinear Science and Numerical Simulation 17:9, pages 3539-3551.
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Seydi Battal Gazi Karakoç & Turabi Geyikli. (2012) Numerical Solution of the Modified Equal Width Wave Equation. International Journal of Differential Equations 2012, pages 1-15.
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Rong Jun Cheng & Hong Xia Ge. (2011) The Meshless Method for Numerical Solution of Modified Equal Width Wave (MEW) Equation. Applied Mechanics and Materials 101-102, pages 1130-1133.
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Turabi Geyikli & Seydi Battal Gazi Karakoc. (2011) Septic B-Spline Collocation Method for the Numerical Solution of the Modified Equal Width Wave Equation. Applied Mathematics 02:06, pages 739-749.
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