scholarly journals Finite difference solutions of the nonlinear Schrödinger equation and their conservation of physical quantities

2007 ◽  
Vol 5 (4) ◽  
pp. 779-788 ◽  
Author(s):  
Clemens Heitzinger ◽  
Christian Ringhofer ◽  
Siegfried Selberherr
Keyword(s):  
Finite Difference ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Physical Quantities

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

2019 ◽  
Vol 30 (12) ◽  
pp. 1950101 ◽  
Author(s):  
Deepika Sharma ◽  
Rohit K. Singla ◽  
Kavita Goyal
Keyword(s):  
Finite Difference ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Differential Operators ◽  
Computational Effort ◽  
Nonlinear Schrodinger Equation ◽  
Computational Time ◽  
Test Problems ◽  
Nonlinear Schrödinger

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 [Formula: see text] (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.

Sign in / Sign up

Export Citation Format

Share Document