TITLE:
A Trapezoidal-Like Integrator for the Numerical Solution of One-Dimensional Time Dependent Schrödinger Equation
AUTHORS:
Johnson Oladele Fatokun
KEYWORDS:
Schrödinger’s Equation, Partial Differential Equations, Method of Lines (MOL), Stiff ODE, Trapezoidal-Like Integrator
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.4 No.4,
August
29,
2014
ABSTRACT: In this paper, the
one-dimensional time dependent Schr?dinger equation is discretized by the method
of lines using a second order finite difference approximation to replace the
second order spatial derivative. The evolving system of stiff Ordinary
Differential Equation (ODE) in time is solved numerically by an L-stable
trapezoidal-like integrator. Results show accuracy of relative maximum error of
order 10?4 in the interval of consideration. The performance of the
method as compared to an existing scheme is considered favorable.