scholarly journals A Wavelet-Galerkin Method for the Nonlinear Schrödinger Equation

2021 ◽  
pp. 81-88
Author(s):  
Yacine Benhadid
Keyword(s):  
Distribution Function ◽  
Nonlinear Equation ◽  
Galerkin Method ◽  
Numerical Solution ◽  
Explicit Formula ◽  
Schrodinger Equation ◽  
Numerical Results ◽  
Wavelet Method ◽  
Wavelet Galerkin Method ◽  
General Behavior

A general implementation is presented for constructing a wavelet method for solving the nonlinear equation of Schr¨odinger. An explicit formula is derived which yields a stability in of the numerical solution. A simulation is elaborated to show the general behavior of the distribution function. Numerical results and comparison with classical algorithms are provided. This approach prove an attractive scheme for solving such equation.

An Accurate Method for the Numerical Solution of the Schrödinger Equation

1997 ◽  
Vol 12 (26) ◽  
pp. 1891-1900 ◽  
Author(s):  
T. E. Simos
Keyword(s):  
Schrödinger Equation ◽  
Numerical Solution ◽  
Numerical Integration ◽  
Schrodinger Equation ◽  
Free Parameter ◽  
Accurate Method ◽  
Numerical Results ◽  
Exponential Functions ◽  
New Methods ◽  
Radial Schrödinger Equation

We present here an accurate method for the numerical integration of the radial Schrödinger equation. The formula considered contains free parameter which are defined in order to integrate exponential functions. Numerical results also indicate that the new methods are much more accurate than other Numerov-type well-known methods.

scholarly journals Numerical Solution of Time Fractional Schrödinger Equation by Using Quadratic B-Spline Finite Elements

2017 ◽  
Vol 31 (1) ◽  
pp. 83-98 ◽  
Author(s):  
Alaattin Esen ◽  
Orkun Tasbozan
Keyword(s):  
Finite Elements ◽  
Schrödinger Equation ◽  
Galerkin Method ◽  
Numerical Solution ◽  
Fractional Order ◽  
Schrodinger Equation ◽  
Numerical Solutions ◽  
B Spline ◽  
Fractional Schrödinger Equation ◽  
Fractional Schrodinger Equation

Abstract In this article, quadratic B-spline Galerkin method has been employed to solve the time fractional order Schrödinger equation. Numerical solutions and error norms L2 and L∞ are presented in tables.

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