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A mixed algorithm for numerical computation of soliton solutions of the coupled KdV equation: Finite difference method and differential quadrature method

Başhan A.

Article | 2019 | Applied Mathematics and Computation360 , pp.42 - 57

The aim of the manuscript is to investigate numerical solutions of the system of coupled Korteweg-de Vries equation. For this approximation, we have used finite difference method for time integration and differential quadrature method depending on modified cubic B-splines for space integration. To display the accuracy of the present mixed method three famous test problems namely single soliton, interaction of two solitons and birth of solitons are solved and the error norms L2 and L? are computed and compared with earlier works. Comparison of error norms show that present mixed method obtained superior results than earlier works by . . .using same parameters and less number of nodal points. At the same time, two lowest invariants and amplitude values of solitons during the simulations are calculated and reported. In addition those, relative changes of invariants are computed and tabulated. Properties of solitons observed clearly at the all of the test problems and figures of the all of the simulations are given. © 2019 Elsevier Inc Daha fazlası Daha az

An inverse problem for the general kinetic equation and a numerical method

Amirov A. | Gölgeleyen F. | Rahmanova A.

Article | 2009 | CMES - Computer Modeling in Engineering and Sciences43 ( 2 ) , pp.131 - 147

This paper has two purposes. The first is to prove existence and uniqueness theorems for the solution of an inverse problem for the general linear kinetic equation with a scattering term. The second one is to develop a numerical approximation method for the solution of this inverse problem for two dimensional case using finite difference method.© 2009 Tech Science Press.

On the solution of an inverse problem for an integro-differential transport equation

Gölgeleyen I.

Article | 2010 | CMES - Computer Modeling in Engineering and Sciences64 ( 1 ) , pp.71 - 89

In this paper, the solvability conditions for an inverse problem for an integro-differential transport equation are obtained and a numerical approximation method based on the finite difference method is developed. A comparison between the numerical solution and the exact solution of the problem is presented. Experimental results show that proposed method is robust to data noises. © 2010 Tech Science Press.

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