Geodesic
Numerical Solution of Shrödinger Equations Based on the Meshless Methods
Kragujevac Journal of Mathematics, Tome 46 (2022) no. 6, p. 929 .

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In this work, two-dimensional time-dependent quantum equation problems are studied. We introduce a numerical algorithm for solving the two-dimensional nonlinear complex quantum system with MLS and FDM methods. An efficient and accurate computational algorithm based on both, the moving least squares (MLS) and the finite difference (FDM) methods is proposed for solving it. The results demonstrate that the proposed algorithm is a robust algorithm with good accuracy. This is developed on MLS and FDM methods using numerical simulation for solving these kind of problems.
Classification : 41A45, 41A25, 65M06
Keywords: Time-dependent quantum equations, moving least squares (MLS) method, finite difference scheme (FDM) 
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     author = {Mojtaba Rahimi and Seyed Mehdi Karbassi and Mohammad reza Hooshm},
     title = {Numerical {Solution} of {Shr\"odinger} {Equations} {Based} on the {Meshless} {Methods}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {929 },
     publisher = {mathdoc},
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     number = {6},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2022_46_6_a7/}
}
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Mojtaba Rahimi; Seyed Mehdi Karbassi; Mohammad reza Hooshm. Numerical Solution of Shrödinger Equations Based on the Meshless Methods. Kragujevac Journal of Mathematics, Tome 46 (2022) no. 6, p. 929 . http://geodesic.mathdoc.fr/item/KJM_2022_46_6_a7/