Abstract: This paper devotes to establishing the optimal error bounds of the finite difference methods for solving the $d$-dimensional ($d$=2,3) nonlinear Klein-Gordon-Schrodinger KGS) equations. The proposed finite difference methods not only conserves the total energy in the discrete level but also are linearized in the practical computation. The error estimates are proved to be independent of the grid ratios and second-order in the discrete $H^{2}$-norm. Numerical results are reported to confirm our theoretical error estimates of the proposed finite difference methods.

报告人简介：王廷春博士，现为南京信息工程大学数学与统计学院信息与计算科学系副教授、硕士生导师，研究方向为偏微分方程数值解和平面动力系统，先后主持一项国家自然科学天元基金和一项国家自然科学青年基金项目，已在《Journal of Computational Physics》、《SCIENCE CHINA Mathematics》、《Journal of Scientific Computing》、《Journal of Computational Mathematics》、《Numerical Methods for Partial Differential Equations》、《Journal of Computational and Applied mathematics》、《中国科学：数学》等杂志发表学术论文20余篇。当前感兴趣的研究方向为高振荡色散问题的数值算法及其收敛性分析。

Date&Time: December 23, 2013 (Monday), 10:45-11:45 a.m.
Location: 606 Conference Room, No.3 Heqing Road, Haidian District