Journal ArticleDOI
Numerical solution of complex modified Korteweg-de Vries equation by collocation method
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TLDR
In this paper, the collocation method using quintic B-spline is derived for solving the complex modified Korteweg-de Vries (CMKdV) problem.About:
This article is published in Communications in Nonlinear Science and Numerical Simulation.The article was published on 2009-03-01. It has received 32 citations till now. The article focuses on the topics: Collocation method & Korteweg–de Vries equation.read more
Citations
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On the selection of a good value of shape parameter in solving time-dependent partial differential equations using RBF approximation method
TL;DR: In this paper, the authors extended the proposed algorithm for selecting a good value of shape parameter c in solving time-dependent partial differential equations, which is directly connected to the accuracy of the method.
Journal ArticleDOI
Free element collocation method: A new method combining advantages of finite element and mesh free methods
TL;DR: A new numerical method, named as the Free Element Collocation Method (FECM), is proposed for solving general engineering problems governed by the second order partial differential equations (PDEs), which can result in more stable results than the traditional collocation method.
Journal ArticleDOI
RBF-PS scheme for solving the equal width equation
TL;DR: The equal width equation is solved by a RBF-PS scheme, and the radial kernels are used to transform the PDE into a system of ODEs.
Journal ArticleDOI
1-Soliton solution of the generalized KdV equation with generalized evolution
M. S. Ismail,Anjan Biswas +1 more
TL;DR: The 1-soliton solution of three variants of the generalized KdV equation with generalized evolution is obtained using the solitary wave ansatz to carry out the integration of such equation.
Journal ArticleDOI
Numerical solution of complex modified Korteweg-de Vries equation by mesh-free collocation method
TL;DR: A mesh-free method based on radial basis functions (RBFs) is proposed for the solution of complex modified Korteweg-de Vries (CMKdV) equation and the results obtained are in good agreement with exact solutions and the earlier work.
References
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BookDOI
Nonlinear partial differential Equations
TL;DR: In this paper, the authors consider a class of reaction diffusion equations, with quasi-linear or fully nonlinear diffusion and strong reaction, and propose a model for the singular phenomenon of blow-up, singularities, and singularity.
Journal ArticleDOI
Galerkin method for the numerical solution of the RLW equation using quintic B-splines
İdris Dağ,Bülent Saka,Dursun Irk +2 more
TL;DR: In this paper, the regularized long wave equation (RLW) is solved numerically by using the quintic B-spline Galerkin finite element method and the same method is applied to the time-split RLW equation.
Journal ArticleDOI
Analytical and numerical aspects of certain nonlinear evolution equations. 1V. numerical modified Korteweg-de Vries equation
Thiab R. Taha,Mark J. Ablowitz +1 more
TL;DR: In this article, the inverse scattering transform is used to approximate the Korteweg-de Vries equation, which can be used in order to approximate various numerical methods, such as Zabusky-Kruskal scheme, hopscotch method, hop-scooter method, local scheme, global scheme, split step Fourier method, Tappert method, and pseudospectral method.
Journal ArticleDOI
Numerical simulation of coupled nonlinear Schrödinger equation
M. S. Ismail,Thiab R. Taha +1 more
TL;DR: In this article, a finite difference method for a numerical simulation of the coupled nonlinear Schrodinger equation was proposed, which is second order in space and conserves the energy exactly.
Journal ArticleDOI
Quartic B-spline collocation method to the numerical solutions of the Burgers’ equation
Bülent Saka,İdris Dağ +1 more
TL;DR: In this article, the effect of the quartic B-splines in the collocation method is sought and numerical comparison of results of both algorithms and some other published numerical results are done by studying three standard problems.
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