A new fourteenth algebraic order finite difference method for the approximate solution of the Schrödinger equation

2016 ◽  
Vol 55 (3) ◽  
pp. 697-716 ◽  
Author(s):  
Jianbin Zhao ◽  
T. E. Simos
Keyword(s):  
Approximate Solution ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Schrödinger Equation ◽  
Difference Method ◽  
Schrodinger Equation ◽  
Algebraic Order

scholarly journals The Hybrid Finite Difference and Moving Boundary Methods for Solving a Linear Damped Nonlinear Schrödinger Equation to Model Rogue Waves and Breathers in Plasma Physics

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Alvaro H. Salas ◽  
S. A. El-Tantawy ◽  
Jairo E. Castillo H.
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Schrödinger Equation ◽  
Plasma Physics ◽  
Difference Method ◽  
Schrodinger Equation ◽  
Moving Boundary ◽  
Rogue Waves ◽  
Nonlinear Schrodinger Equation ◽  
Time Interval

In this paper, the dissipative and nondissipative modulated pulses such as rogue waves (RWs) and breathers (Kuznetsov-Ma breathers and Akhmediev breathers) that can exist and propagate in several fields of sciences, for example, plasma physics, have been analyzed numerically. For this purpose, the fluid dusty plasma equations with taking the kinematic dust viscosity into account are reduced to the linear damped nonlinear Schrödinger equation using a reductive perturbation technique. It is known that this equation is not integrable and, accordingly, does not have analytical solution. Thus, for modelling both dissipative RWs and breathers, the improved finite difference method is introduced for this purpose. It is found that FDM is a good numerical technique for small time interval but for large time interval it becomes sometimes unacceptable. Therefore, to describe these waves accurately, the new improved numerical method is considered, which is called the hybrid finite difference method and moving boundary method (FDM-MBM). This last and updated method gives an accurate and excellent description to many physical results, as it was applied to the dust plasma results and the results were good.

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