A Haar wavelet collocation method for coupled nonlinear Schrödinger–KdV equations

Ömer Oruç (), Alaattin Esen () and Fatih Bulut ()
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Ömer Oruç: Department of Mathematics, Faculty of Arts and Science, Inonu University, 44280 Malatya, Turkey
Alaattin Esen: Department of Mathematics, Faculty of Arts and Science, Inonu University, 44280 Malatya, Turkey
Fatih Bulut: Department of Physics, Faculty of Arts and Science, Inonu University, 44280 Malatya, Turkey

International Journal of Modern Physics C (IJMPC), 2016, vol. 27, issue 09, 1-16

Abstract: In this paper, to obtain accurate numerical solutions of coupled nonlinear Schrödinger–Korteweg-de Vries (KdV) equations a Haar wavelet collocation method is proposed. An explicit time stepping scheme is used for discretization of time derivatives and nonlinear terms that appeared in the equations are linearized by a linearization technique and space derivatives are discretized by Haar wavelets. In order to test the accuracy and reliability of the proposed method L2, L∞ error norms and conserved quantities are used. Also obtained results are compared with previous ones obtained by finite element method, Crank–Nicolson method and radial basis function meshless methods. Error analysis of Haar wavelets is also given.

Keywords: Haar wavelet method; coupled nonlinear Schrödinger–KdV equation; nonlinear phenomena; linearization; numerical solution (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (6)

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DOI: 10.1142/S0129183116501035

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