@Article{cmes.2014.103.049,
AUTHOR = {V. C.  Loukopoulos, G. C.  Bourantas},
TITLE = {Solution of Two-dimensional Linear and Nonlinear Unsteady Schrödinger Equation using “Quantum Hydrodynamics” Formulation with a MLPG Collocation Method},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {103},
YEAR = {2014},
NUMBER = {1},
PAGES = {49--70},
URL = {http://www.techscience.com/CMES/v103n1/27110},
ISSN = {1526-1506},
ABSTRACT = {A numerical solution of the linear and nonlinear time-dependent Schrödinger equation is obtained, using the strong form MLPG Collocation method. Schrödinger equation is replaced by a system of coupled partial differential equations in terms of particle density and velocity potential, by separating the real and imaginary parts of a general solution, called a quantum hydrodynamic (QHD) equation, which is formally analogous to the equations of irrotational motion in a classical fluid. The approximation of the field variables is obtained with the Moving Least Squares (MLS) approximation and the implicit Crank-Nicolson scheme is used for time discretization. For the two-dimensional nonlinear Schrödinger equation, the lagging of coefficients method has been utilized to eliminate the nonlinearity of the corresponding examined problem. A Type-I nodal distribution is used in order to provide convergence for the discrete Laplacian operator used at the governing equation. Numerical results are validated, comparing them with analytical and numerical solutions.},
DOI = {10.3970/cmes.2014.103.049}
}