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International Journal of Computer Mathematics Volume 81, 2004 - Issue 3
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Original Articles

Collocation solution of the Korteweg–de Vries equation using septic splines

A. A. SolimanCorrespondence[email protected]
Pages 325-331 | Received 23 Sep 2003, Published online: 12 May 2010

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Eben Maré, Jules Clement Mba & Edson Pindza. (2017) Discrete singular convolution for the generalized variable-coefficient Korteweg-de Vries equation. Quaestiones Mathematicae 40:2, pages 225-244.
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Turabi Geyikli. (2007) Modelling solitary waves of a fifth-order non-linear wave equation. International Journal of Computer Mathematics 84:7, pages 1079-1087.
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Articles from other publishers (30)

Neslihan ÖZDEMİR & Aydın SEÇER. (2022) Wavelet-based Numerical Approaches for Solving the Korteweg-de Vries (KdV) Equation. Turkish Journal of Mathematics and Computer Science 14:1, pages 44-55.
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Ali Başhan. (2021) Modification of quintic B-spline differential quadrature method to nonlinear Korteweg-de Vries equation and numerical experiments. Applied Numerical Mathematics 167, pages 356-374.
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Xiaofeng Wang, Weizhong Dai & Muhammad Usman. (2021) A high-order accurate finite difference scheme for the KdV equation with time-periodic boundary forcing. Applied Numerical Mathematics 160, pages 102-121.
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Seydi Battal Gazi Karakoc, Asit Saha & Derya Sucu. (2020) A novel implementation of Petrov-Galerkin method to shallow water solitary wave pattern and superperiodic traveling wave and its multistability: Generalized Korteweg-de Vries equation. Chinese Journal of Physics 68, pages 605-617.
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N. Tamang, B. Wongsaijai, T. Mouktonglang & K. Poochinapan. (2020) Novel algorithm based on modification of Galerkin finite element method to general Rosenau-RLW equation in (2 + 1)-dimensions. Applied Numerical Mathematics 148, pages 109-130.
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Seydi Battal Gazi Karakoc. (2018) Numerical solutions of the modified KdV Equation with collocation method. Malaya Journal of Matematik 6:4, pages 835-842.
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Seydi Battal Gazi Karakoc. (2018) NUMERICAL SOLUTIONS OF THE MKdV EQUATION VIA COLLOCATION FINITE ELEMENT METHOD. Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi - B Teorik Bilimler, pages 1-1.
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Dursun Irk. (2017) QUINTIC B-SPLINE GALERKIN METHOD FOR THE KdV EQUATION. Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi - B Teorik Bilimler, pages 1-1.
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Mehrdad Lakestani. (2017) Numerical Solutions of the KdV Equation Using B-Spline Functions. Iranian Journal of Science and Technology, Transactions A: Science 41:2, pages 409-417.
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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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Md. Nur Alam & Fethi Bin Muhammad Belgacem. (2016) New Generalized (G'/G)-Expansion Method Applications to Coupled Konno-Oono Equation. Advances in Pure Mathematics 06:03, pages 168-179.
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Ozlem Ersoy & Idris Dag. (2015) The Exponential Cubic B-Spline Algorithm for Korteweg-de Vries Equation. Advances in Numerical Analysis 2015, pages 1-8.
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Kanyuta Poochinapan, Ben Wongsaijai & Thongchai Disyadej. (2014) Efficiency of High-Order Accurate Difference Schemes for the Korteweg-de Vries Equation. Mathematical Problems in Engineering 2014, pages 1-8.
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Mustafa Inc, Ali Akgül & Adem Kiliçman. (2013) A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method. Abstract and Applied Analysis 2013, pages 1-11.
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Mustafa Inc. 2011. Mathematics of Complexity and Dynamical Systems. Mathematics of Complexity and Dynamical Systems 908 923 .
Alper Korkmaz. (2009) Numerical algorithms for solutions of Korteweg–de Vries equation. Numerical Methods for Partial Differential Equations 26:6, pages 1504-1521.
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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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Ahmet Yildirim & Murat Erşen Berberler. (2010) Homotopy perturbation method for numerical solutions of KdV‐Burgers' and Lax's seventh‐order KdV equations. Numerical Methods for Partial Differential Equations 26:5, pages 1040-1053.
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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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A.A. Soliman, A.H.A. Ali & K.R. Raslan. (2009) Numerical solution for the KdV equation based on similarity reductions. Applied Mathematical Modelling 33:2, pages 1107-1115.
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Mustafa Inc. 2022. Solitons. Solitons 161 179 .
Mustafa Inc. 2009. Encyclopedia of Complexity and Systems Science. Encyclopedia of Complexity and Systems Science 5161 5176 .
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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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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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.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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M.T. Darvishi, S. Kheybari & F. Khani. (2006) A numerical solution of the Korteweg-de Vries equation by pseudospectral method using Darvishi’s preconditionings. Applied Mathematics and Computation 182:1, pages 98-105.
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A.A. Soliman. (2006) A numerical simulation and explicit solutions of KdV-Burgers? and Lax?s seventh-order KdV equations. Chaos, Solitons & Fractals 29:2, pages 294-302.
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H. Jafari, Mohammad A. Firouzjaei & Mohammad Saidy. (2008) Comparison Homotopy Analysis Method and Variational Iteration Method for KdV Equation. SSRN Electronic Journal.
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