Efficient Numerical Methods for Solving Coupled Nonlinear Non-stationary Schrödinger Equation

Student: Zakharov Andrey

Educational Programme: Applied Mathematics and Information Science (Bachelor)

Final Grade: 8

Year of Graduation: 2016

Systems of nonlinear Schrödinger equations are widely used for modeling various phenomena in nonlinear fiber optics. In this paper, firstly, examines linear, implicit conservative difference method for numerical solution of a system of two nonlinear and nonstationary Schrödinger equations. It has second-order accuracy in space and time. Secondly, constructs the difference method of fourth-order accuracy in space. The methods are implemented in software, carried out numerical experiments and method's comparisons. Used Richardson extrapolation for constructing method of fourth-order accuracy in time. These methods are also used for the numerical solution of a system of four nonlinear and nonstationary Schrödinger equations.

Full text (added May 26, 2016)

Student Theses at HSE must be completed in accordance with the University Rules and regulations specified by each educational programme.

Summaries of all theses must be published and made freely available on the HSE website.

The full text of a thesis can be published in open access on the HSE website only if the authoring student (copyright holder) agrees, or, if the thesis was written by a team of students, if all the co-authors (copyright holders) agree. After a thesis is published on the HSE website, it obtains the status of an online publication.

Student theses are objects of copyright and their use is subject to limitations in accordance with the Russian Federation’s law on intellectual property.

In the event that a thesis is quoted or otherwise used, reference to the author’s name and the source of quotation is required.

Search all student theses