A Trapezoidal-Like Integrator for the Numerical Solution of One-Dimensional Time Dependent Schrödinger Equation

Johnson Oladele Fatokun

Department of Mathematical Science and Information Technology, Federal University, Dutsin-Ma, Nigeria.

DOI: 10.4236/ajcm.2014.44023                

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.

Keywords

Schrödinger’s Equation, Partial Differential Equations, Method of Lines (MOL), Stiff ODE, Trapezoidal-Like Integrator

Conflicts of Interest

The authors declare no conflicts of interest.

References

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