Numerical solution of time-dependent Schrodinger equation by combination of the finite difference method and particle swarm optimization

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

In this paper, a new numerical method is introduced to solve the time-dependent nonlinear Schrödinger equation. The proposed method is a combination of a novel metaheuristic optimization algorithm with the finite difference method. First, the regarded Schrödinger equation with the ralated boundary and initial conditions are converted into an unconstrained problem. For this purpose, the boundary and initial conditions are satisfied using the penalty method and a proper objective function is defined through the discretized governing equation. Then, a successful version of the particle swarm optimization is implemented to minimize the identified error function and find the best nodal values. The simulation results for several cases are illustrated to depict the effectiveness and capability of the introduced sterategy for solving the time-dependent nonlinear Schrödinger equation.

Language:
Persian
Published:
Journal of Research on Many - body Systems, Volume:11 Issue: 1, 2021
Pages:
114 to 127
https://www.magiran.com/p2345705  
سامانه نویسندگان
  • Corresponding Author (1)
    Mohammad Javad Mahmoodabadi
    Associate Professor Mechanical Engineering,
    Mahmoodabadi، Mohammad Javad
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