The use of a meshless technique based on collocation and radial basis functions for solving the time fractional nonlinear Schrodinger equation arising in quantum mechanics

Akbar Mohebbi; Mostafa Abbaszadeh; Mehdi Dehghan

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The use of a meshless technique based on collocation and radial basis functions for solving the time fractional nonlinear Schrodinger equation arising in quantum mechanics

机译：使用基于搭配和径向基函数的无网格技术求解量子力学中出现的时间分数非线性Schrodinger方程

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摘要

In this paper, we propose a numerical method for the solution of the time-fractional nonlinear Schrodinger equation in one and two dimensions which appear in quantum mechanics. In this method we first approximate the time fractional derivative of the mentioned equation by a scheme of order 0(τ~(2-α), 0 < α < 1 then we will use the Kansa approach to approximate the spatial derivatives. The meshless method has already proved successful in standard quantum mechanics as well as for several other engineering and physical problems. The aim of this paper is to show that the meshless method based on the radial basis functions and collocation approach is also suitable for the treatment of the fractional quantum mechanics. The results of numerical experiments are compared with analytical solution to confirm the accuracy and efficiency of the presented scheme.

机译：在本文中，我们提出了一种求解量子力学中出现的一维和二维时间分数阶非线性薛定inger方程的数值方法。在这种方法中，我们首先通过阶数为0（τ〜（2-α），0 <α<1的方案来近似上述方程式的时间分数导数，然后我们将使用Kansa方法来近似空间导数。已经证明在标准量子力学以及其他几个工程和物理问题上都是成功的，本文的目的是证明基于径向基函数和搭配方法的无网格方法也适用于分数量子的处理。将数值实验的结果与解析解进行比较，以确认所提出方案的准确性和效率。

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来源
《Engineering analysis with boundary elements》 |2013年第2期|475-485|共11页
作者
Akbar Mohebbi; Mostafa Abbaszadeh; Mehdi Dehghan;
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作者单位

Department of Applied Mathematics, Faculty of Mathematical Science, University of Kashan, Kashan, Iran;

Department of Applied Mathematics, Faculty of Mathematical Science, University of Kashan, Kashan, Iran;

Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., 15914 Tehran, Iran;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
time fractional; nonlinear schroedinger equation; kansa method; radial basis functions (RBFs); interpolation method; fractional quantum mechanics; meshless methods;

机译：时间分数非线性薛定inger方程;堪萨法径向基函数（RBF）;插值法分数量子力学无网格方法;

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机译：基于径向基函数的无网格离散配点方法求解分数阶随机积分-微分方程的数值解
2. On the numerical solution of fractional stochastic integro-differential equations via meshless discrete collocation method based on radial basis functions [J] . Mirzaee Farshid, Samadyar Nasrin Engineering analysis with boundary elements . 2019,第Mara期

机译：基于径向基函数的无网状离散搭配方法在分数随机积分 - 微分方程的数值解
3. Two numerical meshless techniques based on radial basis functions (RBFs) and the method of generalized moving least squares (GMLS) for simulation of coupled Klein-Gordon-Schrodinger (KGS) equations [J] . Dehghan Mehdi, Mohammadi Vahid Computers & mathematics with applications . 2016,第4期

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4. Least-Squares Collocation Points Meshless Method with Radial Basis Functions Solving Elliptic Equations [C] . Baoshan Miao, Xinqiang Qin, Gang Hu, ISAI 2010;International conference on information security and artificial intelligence . 2010

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5. Accelerating the performance of a novel meshless method based on collocation with radial basis functions by employing a graphical processing unit as a parallel coprocessor. [D] . Owusu-Banson, Derek. 2012

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6. Optimal Control of Time-Delay Fractional Equations via a Joint Application of Radial Basis Functions and Collocation Method [O] . Shu-Bo Chen, Samaneh Soradi-Zeid, Hadi Jahanshahi, 2020

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7. Numerical Study of Astrophysics Equations by Meshless Collocation Method Based on Compactly Supported Radial Basis Function [O] . Parand, Kourosh, Hemami, Mohammad 2016

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The use of a meshless technique based on collocation and radial basis functions for solving the time fractional nonlinear Schrodinger equation arising in quantum mechanics

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