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.
Highlights
Numerical methods have played an important role in researches in physics
According to [1], numerical methods of Partial Differential Equations (PDEs) have played an important role in various areas of mathematical physics
In numerical relativity a set of highly nonlinear systems of coupled differential equations of general relativity have to be solved under very general symmetry conditions in order to predict the profile of gravitational waves expected to be observed by ground-based gravitational wave detectors
Summary
Numerical methods have played an important role in researches in physics. Most often Partial Differential Equations (PDEs) are used to model physical problems. According to [1], numerical methods of PDEs have played an important role in various areas of mathematical physics. (2014) A Trapezoidal-Like Integrator for the Numerical Solution of One-Dimensional Time Dependent Schrödinger Equation. In the evolution of a Bose condensate, the solution of the time dependent Schrodinger equation involved is sought for by numerical method. We shall discretize the 1-dimensional Schrödinger equation by the Method of Lines (MOL). The numerical solution of the resulting system of coupled stiff Ordinary Differential Equations (ODEs) shall be sought for using an L-stable implicit trapezoidal-like integrator.
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