 Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devicesMehdi Dehghan Mathematics and Computers in Simulation (MATCOM), 2006, vol. 71, issue 1, 16-30 Abstract: Several finite difference schemes are discussed for solving the two-dimensional Schrodinger equation with Dirichlet’s boundary conditions. We use three fully implicit finite difference schemes, two fully explicit finite difference techniques, an alternating direction implicit procedure and the Barakat and Clark type explicit formula. Theoretical and numerical comparisons between four families of methods are described. The main advantage of the alternating direction implicit finite difference technique is that the bandwidth of the sets of equations is a fixed small number that depends only on the nature of the computational molecule. This allows the use of very efficient and very fast techniques for solving the resulting tridiagonal systems of linear algebraic equations. The unique advantage of the Barakat and Clark technique is that it is unconditionally stable and is explicit in nature. Numerical results are presented followed by concluding remarks. Keywords: Two-dimensional schrodinger equation; Electro-magnetic waves; Finite difference methods; Dirichlet’s boundary conditions; Optoelectronic devices (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:71:y:2006:i:1:p:16-30 DOI: 10.1016/j.matcom.2005.10.001 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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