استفاده از روشهای تفاضل متناهی غیر استاندارد برای حل معادله شرودینگر تبدیل شده به ODE
Subject Areas : Numerical Analysis
فرنوش ایزدی
1
(
دانشکده ریاضی، گروه ریاضی کاربردی، دانشگاه آزاد اسلامی واحد صومعه سرا، صومعه سرا، ایران
)
Keywords: سازگاری, پایداری, معادله شرودینگر, تفاضل متناهی, روش غیر استاندارد,
Abstract :
Agrawal, G. P. (2001). Nonlinear fiber optics,3rd.,Academic press Sandiego,(2001).
Anguelov, R., & Lubuma, J. M. S. (2003). Nonstandard finite difference method by nonlocal approximation. Mathematics and Computers in simulation, 61(3-6), 465-475.
Bao, W. (2004). Numerical methods for the nonlinear Schrödinger equation with nonzero far-field conditions. Methods and applications of analysis, 11(3), 367-388.
Bao, W., & Jaksch, D. (2003). An explicit unconditionally stable numerical method for solving damped nonlinear Schrödinger equations with a focusing nonlinearity. SIAM Journal on Numerical Analysis, 41(4), 1406-1426.
Boris, M. (2005). Nonlinear schrodinger equations. Scott, Alwyn, Encyclopedia of Nonlinear Science, New York: Routledge, 639-643.
Dehghan, M., & Taleei, A. (2010). Numerical solution of nonlinear Schrödinger equation by using time‐space pseudo‐spectral method. Numerical Methods for Partial Differential Equations: An International Journal, 26(4), 979-992.
Fordy, A. P. (1990). Solution theory :asurvay of results, Manchester university press,Manchester.
Laloë, F. (2019). Do we really understand quantum mechanics?. Cambridge University Press.
Mickens, R. E. (1989). Stable explicit schemes for equations of Schrödinger type. Physical Review A, 39(11), 5508.
Mickens, R. E. (1994). Nonstandard finite difference models of differential equations. world scientific.
Mickens, R. E. (2000). Applications of nonstandard finite difference schemes. World Scientific.
Mickens, R. E. (2002). Nonstandard finite difference schemes for differential equations. Journal of Difference Equations and Applications, 8(9), 823-847.
Mickens, R. E. (2005). Advances in the applications of nonstandard finite difference schemes. World Scientific.
Schrödinger, E. (1926). An undulatory theory of the mechanics of atoms and molecules. Physical review, 28(6), 1049.
Stenflo, L., & Yu, M. Y. (1997). Nonlinear wave modulation in a cylindrical plasma. IEEE transactions on plasma science, 25(5), 1155-1157.
Sulem. C., & Sulem, P.L. (1999). The nonlinear shrodinger equation: self-fousing and wave collaps, Springer,Newyork.
Wazwaz, A. M. (2010). Partial differential equations and solitary waves theory. Springer Science & Business Media.