An adaptive grid-based curvelet optimized solution for nonlinear Schrödinger equation

Deepika Sharma, Rohit K. Singla () and Kavita Goyal ()
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Deepika Sharma: #x2020;School of Mathematics, Thapar Institute of Engineering and Technology, Patiala, Punjab, India
Rohit K. Singla: Mechanical Engineering Department, Thapar Institute of Engineering and Technology, Patiala, Punjab, India
Kavita Goyal: #x2020;School of Mathematics, Thapar Institute of Engineering and Technology, Patiala, Punjab, India

International Journal of Modern Physics C (IJMPC), 2019, vol. 30, issue 12, 1-28

Abstract: In this work, a dynamically adaptive curvelet technique has been developed for solving nonlinear Schrödinger equation (NLS). Central finite difference method is used for approximating the one- and two-dimensional differential operators and radial-basis functions (RBFs) are utilized for approximating the differential operators on the sphere. The grid on which the equation is solved, is obtained using curvelets. For test problems 1 and 2 (1d & 2d problems) considered in this paper, the computational time carried out by the proposed technique is analyzed with the computational time carried out by the finite difference technique. Moreover, the problem on the sphere has been considered, for which the computational time carried out by the RBF collocation technique is analyzed with the computational time carried out by the proposed technique. It is found that the developed technique performs better in terms of computational time, for example, on sphere, computational effort reduces by four times using the proposed method.

Keywords: Curvelet; adaptive grid; multiresolution analysis (MRA); Schrödinger equation (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S0129183119501018

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