Thesis Defense - Batuhan Bayır (MSMATH)

Batuhan Bayır – M.Sc. Mathematics

Assoc. Prof. Handan Borluk – Advisor

Date: 24.05.2023

Time: 10.30

Location: AB1 414

“ANALYSIS OF A FULLY DISCRETE FOURIER PSEUDOSPECTRAL METHOD FOR THE ROSENAU EQUATION”

Assoc. Prof. Handan Borluk, Özyeğin University

Prof. Hüsnü Ata Erbay, Özyeğin University

Assoc. Prof. Ali Demirci, İstanbul Technical University

Abstract:

In this thesis study, we consider the Rosenau equation with a single power type nonlinearity. The Rosenau equation is proposed as an alternative to the celebrated Korteweg–de Vries (KdV) equation. It describes the propagation of waves in the anharmonic crystal lattice. This equation possesses a solitary wave solutions when the order of nonlinear term and speed of the wave is greater than 1. However, there is no exact solution in the literature in the case of single-power type nonlinearity. Therefore, the numerical investigation of the equation becomes important to understand the dynamics of the waves. There are numerical studies in the literature mostly using the methods like finite difference and finite element methods. Moreover, most of these studies focus on the numerical analysis of the scheme and do not present numerical experiments. We propose a numerical scheme combining Fourier pseudospectral method and a second-order finite difference method. We also present the truncation error and stability analysis of the proposed scheme. We then introduce some numerical experiments to verify the theoretical results. For this aim, we generate the solitary wave solutions by the Petviashvili iteration method then we observe the evolution of these waves using the proposed scheme.

Bio:

Batuhan Bayır completed his undergraduate degree in Physics at Ankara University in 2021. He is a graduate student in the Mathematics program at Özyeğin University and is interested in partial differential equations.