Rosenau denklemi için tam kesikli Fourier spektral metod ve analizi

In this thesis study, we consider the Rosenau equation with a single power type nonlinear term. The Rosenau equation is proposed as an alternative to the celebrated Korteweg–de Vries (KdV) equation. It describes the propagation of nonlinear waves in anharmonic crystal lattices. This equation possesses solitary wave solutions when the order of nonlinear term and wave speed is greater than 1. However, an exact solution is not available in the literature when the nonlinear term is single power type. Therefore, the numerical investigation of the equation becomes important to understand the dynamics of the waves. There are many numerical studies in the literature mostly using the finite difference and finite element methods. Moreover, most of these studies focus on the numerical analysis of the scheme and do not present numerical results. In this work, we present a numerical scheme combining the Fourier pseudospectral method and second order finite difference method. We also present the truncation error and stability analysis of the proposed scheme. We then introduce some numerical results to verify the theoretical analysis. For this aim, we derive initial solitary wave profiles with the Petviashvili iteration method. Then, we observe the evolution of these solutions using the proposed scheme.