Lineer Olmayan bir Schrödinger Denkleminin Galerkin Metoduyla Çözümü

Year 2017, Volume: 7 Issue: 2, 225 - 239, 30.06.2017

Nigar Yıldırım Aksoy

Abstract

Bu çalışmada iki boyutlu lineer olmayan bir Schrödinger denklemi için bir başlangıç sınır değer problemi
göz önüne alırız. Galerkin metodunu kullanarak başlangıç sınır değer probleminin çözümünün var ve tek olduğunu
ispatlarız. Ayrıca, başlangıç sınır değer probleminin çözümü için bir değerlendirme elde ederiz.

Keywords

Başlangıç sınır değer problemi, Galerkin metodu, Schrödinger denklemi

Solution of a Nonlinear Schrödinger Equation with Galerkin’s Method

Abstract

In this paper, we consider an initial boundary value problem for a two-dimensional nonlinear
Schrödinger equation. We prove by using Galerkin’s method that the solution of the initial boundary value problem
exists and it has a unique solution. Also, we get an estimation for the solution of the initial boundary value problem.

Keywords

Galerkin method, initial boundary value problem, Schrödinger equation

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