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International Journal of Computer Mathematics Volume 78, 2001 - Issue 3
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Original Articles

Collocation method using quadratic B-spline for the RLW equation

A.A. Soliman Dept. of Math., Fac. of Edu, (Al-Arish) Suez Canal Univ.,
&
K.R. Raslan Dept. of Math., Fac. of Sci, Al-Azhar Univ, Nasr-City, Cairo, 11884, Egypt
Pages 399-412 | Received 29 Mar 2000, Published online: 19 Mar 2007

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Seydi Battal Gazi Karakoç, Liquan Mei & Khalid K. Ali. (2022) Two efficient methods for solving the generalized regularized long wave equation. Applicable Analysis 101:13, pages 4721-4742.
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Hany N. Hassan. (2017) An efficient numerical method for the modified regularized long wave equation using Fourier spectral method. Journal of the Association of Arab Universities for Basic and Applied Sciences 24:1, pages 198-205.
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M.M. Hosseini, H. Ghaneai, Syed Tauseef Mohyud-Din & Muhammad Usman. (2016) Tri-prong scheme for regularized long wave equation. Journal of the Association of Arab Universities for Basic and Applied Sciences 20:1, pages 68-77.
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A. A. Soliman. (2004) Numerical scheme based on similarity reductions for the regularized long wave equation. International Journal of Computer Mathematics 81:10, pages 1281-1288.
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Articles from other publishers (54)

Xingxia Liu, Lijun Zhang & Jianan Sun. (2024) Numerical Analysis of the Discrete MRLW Equation for a Nonlinear System Using the Cubic B-Spline Collocation Method. Symmetry 16:4, pages 438.
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Melike KARTA. (2023) Numerical approximation with the splitting algorithm to a solution of the modified regularized long wave equation. Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 72:4, pages 1034-1054.
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Nabendra Parumasur, Rasheed A. Adetona & Pravin Singh. (2023) Efficient Solution of Burgers’, Modified Burgers’ and KdV–Burgers’ Equations Using B-Spline Approximation Functions. Mathematics 11:8, pages 1847.
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Wenjie Wu, Jalil Manafian, Khalid K. Ali, Seydi Battal Gazi Karakoc, Abbas H. Taqi & Muhannad A. Mahmoud. (2022) Numerical and analytical results of the 1D BBM equation and 2D coupled BBM-system by finite element method. International Journal of Modern Physics B 36:28.
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Jianguo Ren, Jalil Manafian, Muhannad A. Shallal, Hawraz N. Jabbar & Sizar A. Mohammed. (2022) Quintic B-spline collocation method for the numerical solution of the Bona–Smith family of Boussinesq equation type. International Journal of Nonlinear Sciences and Numerical Simulation 23:1, pages 135-148.
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Seydi Battal Gazi Karakoc & Khalid Karam Ali. (2021) Theoretical and computational structures on solitary wave solutions of Benjamin Bona Mahony-Burgers equation. Tbilisi Mathematical Journal 14:2.
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Hang Zheng, Yonghui Xia, Yuzhen Bai & Luoyi Wu. (2021) Travelling Wave Solutions of the General Regularized Long Wave Equation. Qualitative Theory of Dynamical Systems 20:1.
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Asma Rouatbi, Manel Labidi & Khaled Omrani. (2021) Conservative Difference Scheme of Solitary Wave Solutions of the Generalized Regularized Long-Wave Equation. Indian Journal of Pure and Applied Mathematics 51:4, pages 1317-1342.
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Qi Hong, Yushun Wang & Yuezheng Gong. (2019) Optimal error estimate of two linear and momentum‐preserving Fourier pseudo‐spectral schemes for the RLW equation. Numerical Methods for Partial Differential Equations 36:2, pages 394-417.
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Seydi Battal Gazi Karakoc & Samir Kumar Bhowmik. (2019) Galerkin finite element solution for Benjamin–Bona–Mahony–Burgers equation with cubic B-splines. Computers & Mathematics with Applications 77:7, pages 1917-1932.
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Necdet Bildik & Sinan Deniz. (2017) Solving the burgers' and regularized long wave equations using the new perturbation iteration technique. Numerical Methods for Partial Differential Equations 34:5, pages 1489-1501.
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Hamad Salih, Luma Naji Mohammed Tawfiq, Zainor Ridzuan Yahya & Shazalina Mat Zin. (2018) Solving Modified Regularized Long Wave Equation Using Collocation Method. Journal of Physics: Conference Series 1003, pages 012062.
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Abdel-Maksoud A. Soliman. (2017) Collocation Method using Quartic B-Splines for Solving the Modified RLW Equation. Indian Journal of Science and Technology 10:31, pages 1-7.
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Xintian Pan & Luming Zhang. (2016) On the convergence of a high-accuracy compact conservative scheme for the modified regularized long-wave equation. SpringerPlus 5:1.
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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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S. Battal Gazi Karakoç & Halil Zeybek. (2016) Solitary-wave solutions of the GRLW equation using septic B-spline collocation method. Applied Mathematics and Computation 289, pages 159-171.
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Md. Nur Alam & Cemil Tunc. (2016) An analytical method for solving exact solutions of the nonlinear Bogoyavlenskii equation and the nonlinear diffusive predator–prey system. Alexandria Engineering Journal 55:2, pages 1855-1865.
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J I Ramos. (2016) On the accuracy of some explicit and implicit methods for the inviscid GRLW equation subject to initial Gaussian conditions. International Journal of Numerical Methods for Heat & Fluid Flow 26:3/4, pages 698-721.
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Rakesh Kumar & S. Baskar. (2016) B-spline quasi-interpolation based numerical methods for some Sobolev type equations. Journal of Computational and Applied Mathematics 292, pages 41-66.
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Xintian Pan, Haitao Che & Yiju Wang. (2015) A high-accuracy compact conservative scheme for generalized regularized long-wave equation. Boundary Value Problems 2015:1.
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Liquan Mei, Yali Gao & Zhangxin Chen. (2015) Numerical study using explicit multistep G alerkin finite element method for the MRLW equation . Numerical Methods for Partial Differential Equations 31:6, pages 1875-1889.
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Reza Mohammadi. (2015) Exponential B-spline collocation method for numerical solution of the generalized regularized long wave equation. Chinese Physics B 24:5, pages 050206.
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S. Demiray, Ö. Ünsal & A. Bekir. (2014) New Exact Solutions for Boussinesq Type Equations by Using (G'/G, 1/G) and (1/G')-Expansion Methods. Acta Physica Polonica A 125:5, pages 1093-1098.
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Seydi Battal Gazi Karakoç, Turgut Ak & Halil Zeybek. (2014) An Efficient Approach to Numerical Study of the MRLW Equation with B-Spline Collocation Method. Abstract and Applied Analysis 2014, pages 1-15.
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Liquan Mei, Yali Gao & Zhangxin Chen. (2014) A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave Equation. Abstract and Applied Analysis 2014, pages 1-11.
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Givi Berikelashvili & Manana Mirianashvili. (2013) On the convergence of difference schemes for generalized Benjamin–Bona–Mahony equation. Numerical Methods for Partial Differential Equations 30:1, pages 301-320.
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Seydi Battal Gazi Karakoc & Turabi Geyikli. (2013) Petrov-Galerkin finite element method for solving the MRLW equation. Mathematical Sciences 7:1.
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Seydi Battal Gazi Karakoc, Nuri Murat Yagmurlu & Yusuf Ucar. (2013) Numerical approximation to a solution of the modified regularized long wave equation using quintic B-splines. Boundary Value Problems 2013:1.
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Y. Khan, R. Taghipour, M. Falahian & A. Nikkar. (2012) A new approach to modified regularized long wave equation. Neural Computing and Applications 23:5, pages 1335-1341.
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Liquan Mei & Yaping Chen. (2012) Numerical solutions of RLW equation using Galerkin method with extrapolation techniques. Computer Physics Communications 183:8, pages 1609-1616.
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D. Irk. (2012) Solitary wave solutions for the regularized long-wave equation. Physics of Wave Phenomena 20:3, pages 174-183.
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Liquan Mei & Yaping Chen. (2012) Explicit multistep method for the numerical solution of RLW equation. Applied Mathematics and Computation 218:18, pages 9547-9554.
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Yilmaz Dereli. (2011) Solitary wave solutions of the MRLW equation using radial basis functions. Numerical Methods for Partial Differential Equations 28:1, pages 235-247.
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Zi-Liang Li. (2010) Constructing of new exact solutions to the GKdV–mKdV equation with any-order nonlinear terms by -expansion method. Applied Mathematics and Computation 217:4, pages 1398-1403.
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Mohamed Hayek. (2010) Constructing of exact solutions to the KdV and Burgers equations with power-law nonlinearity by the extended -expansion method. Applied Mathematics and Computation 217:1, pages 212-221.
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K.R. Raslan & Talaat S. EL-Danaf. (2010) Solitary waves solutions of the MRLW equation using quintic B-splines. Journal of King Saud University - Science 22:3, pages 161-166.
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K.R. Raslan. (2009) Numerical study of the Modified Regularized Long Wave (MRLW) equation. Chaos, Solitons & Fractals 42:3, pages 1845-1853.
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Li Zi-Liang. (2009) Application of higher-order KdV-mKdV model with higher-degree nonlinear terms to gravity waves in atmosphere. Chinese Physics B 18:10, pages 4074-4082.
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K.R. Raslan & Saleh M. Hassan. (2009) Solitary waves for the MRLW equation. Applied Mathematics Letters 22:7, pages 984-989.
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S. Pak. (2009) Solitary Wave Solutions for the RLW Equation by He's Semi inverse Method. International Journal of Nonlinear Sciences and Numerical Simulation 10:4.
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A. A. Soliman. (2008) Extended Improved tanh-Function Method for Solving the Nonlinear Physical Problems. Acta Applicandae Mathematicae 104:3, pages 367-383.
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Bülent Saka & İdris Dağ. (2007) A numerical solution of the RLW equation by Galerkin method using quartic B‐splines. Communications in Numerical Methods in Engineering 24:11, pages 1339-1361.
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Zi-Liang Li. (2008) Solitary wave and periodic wave solutions for the thermally forced gravity waves in atmosphere. Journal of Physics A: Mathematical and Theoretical 41:14, pages 145206.
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A.K. Khalifa, K.R. Raslan & H.M. Alzubaidi. (2008) A collocation method with cubic B-splines for solving the MRLW equation. Journal of Computational and Applied Mathematics 212:2, pages 406-418.
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Emmanuel Yomba. (2008) A generalized auxiliary equation method and its application to nonlinear Klein–Gordon and generalized nonlinear Camassa–Holm equations. Physics Letters A 372:7, pages 1048-1060.
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A.A. Soliman. (2007) Exact traveling wave solution of nonlinear variants of the RLW and the PHI-four equations. Physics Letters A 368:5, pages 383-390.
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A.K. Khalifa, K.R. Raslan & H.M. Alzubaidi. (2007) A finite difference scheme for the MRLW and solitary wave interactions. Applied Mathematics and Computation 189:1, pages 346-354.
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A.H.A. Ali. (2007) The modified extended tanh-function method for solving coupled MKdV and coupled Hirota–Satsuma coupled KdV equations. Physics Letters A 363:5-6, pages 420-425.
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A. Esen & S. Kutluay. (2006) Application of a lumped Galerkin method to the regularized long wave equation. Applied Mathematics and Computation 174:2, pages 833-845.
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S. Kutluay & A. Esen. (2006) A finite difference solution of the regularized long-wave equation. Mathematical Problems in Engineering 2006, pages 1-14.
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A.A. Soliman. (2005) Numerical simulation of the generalized regularized long wave equation by He’s variational iteration method. Mathematics and Computers in Simulation 70:2, pages 119-124.
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K.R. Raslan. (2005) Collocation method using quartic B-spline for the equal width (EW) equation. Applied Mathematics and Computation 168:2, pages 795-805.
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A.A. Soliman & M.H. Hussien. (2005) Collocation solution for RLW equation with septic spline. Applied Mathematics and Computation 161:2, pages 623-636.
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K. Djidjeli, W. G. Price, E. H. Twizell & Q. Cao. (2003) A linearized implicit pseudo‐spectral method for some model equations: the regularized long wave equations. Communications in Numerical Methods in Engineering 19:11, pages 847-863.
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