报告题目：A Numerical Method for Solving the Nonlinear Fermi–Pasta–Ulam Problem

报告人：任金城教授 （河南财经政法大学）

时间：2018年6月19日10:00-11:00

听众：计算数学部分研究生

地点：金融实验室

摘要An effective finite difference scheme for solving the nonlinear Fermi–Pasta–Ulam (FPU) problem is derived. The most important feature of the scheme inherits energy conservation property from the nonlinear FPU problem. The unique solvability and the convergence of the difference scheme are proved by the energy method. The convergence order is $O(\tau^2 + h^2)$ in the maximum norm, where $\tau$ is the temporal grid size and $h$ is the spatial grid size, respectively. In addition, the stability of the difference scheme is obtained. Numerical results are presented to support the theoretical analysis and verify numerically the energy conservation property.

任金城，男，副教授，河南南阳人，河南财经政法大学数学与信息科学学院工作。先后被评为河南省高校科技创新人才、河南省教育厅学术技术带头人，河南财经政法大学青年拔尖人才等称号。现主要从事分数阶偏微分方程的数值算法研究, 主持国家自然科学基金项目2项，省高校科技创新人才项目1项，省厅级项目6项，获得省厅级奖励8项。在国际SCI期刊Journal of Computational Physics和Journal of Scientific Computing等杂志发表论文二十余篇。