Numerical Solution of Nonlinear Schrödinger Equation with Neumann Boundary Conditions Using Quintic B-Spline Galerkin Method

Symmetry

Azhar Iqbal¹  AhmadIzani Md. Ismail²  NurNadiah Abd Hamid² 

[1] Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, 31952 Al Khobar, Saudi Arabia;School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia;

关键词: non-linear Schrödinger equation;    quintic B-spline;    Galerkin finite element method;   

DOI  :  10.3390/sym11040469

来源: DOAJ

【 摘 要 】

This paper is concerned with the numerical solution of the nonlinear Schrödinger (NLS) equation with Neumann boundary conditions by quintic B-spline Galerkin finite element method as the shape and weight functions over the finite domain. The Galerkin B-spline method is more efficient and simpler than the general Galerkin finite element method. For the Galerkin B-spline method, the Crank Nicolson and finite difference schemes are applied for nodal parameters and for time integration. Two numerical problems are discussed to demonstrate the accuracy and feasibility of the proposed method. The error norms $L_2$ , $L_{\infty }$ and conservation laws $I_1, I_2$ are calculated to check the accuracy and feasibility of the method. The results of the scheme are compared with previously obtained approximate solutions and are found to be in good agreement.

【 授权许可】

Unknown