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Discrete maximum principle of exponential time differencing schemes for nonlocal Allen-Cahn equations
发布时间: 2018-04-17     19:22   【返回上一页】 发布人:乔中华


北京师范大学数学科学学院

 

计算数学学术报告

 

 

报告题目:Discrete maximum principle of exponential time differencing schemes for nonlocal Allen-Cahn equations

 

报告人:乔中华教授(香港理工大学)

 

时间地点:4月24日 2:00-3:00 后主楼1223

 

邀请人:张辉

 

报告摘要:In this work, we construct exponential time differencing (ETD) schemes for solving the nonlocal Allen-Cahn (NAC) equation. Since the solution to the NAC equation satisfies the maximum principle, numerical approximations preserving the maximum principle in the discrete sense are highly desirable at both physical and mathematical levels. Our numerical schemes are obtained by using the quadrature-based finite difference method for the spatial discretization and applying ETD-based approximations on the temporal integration. We establish the discrete maximum principle by using the properties of matrix exponentials, and then the energy stability and the maximum-norm error estimates are obtained in the discrete sense. In addition, we also prove the asymptotic compatibility of the proposed scheme, which implies the robustness of numerical approximations to the NAC equation. The convergence rates are verified numerically with respect to the discretization and the nonlocal parameters. A further numerical investigation is carried out for the steady state solutions on the relationship between the discontinuities and the nonlocal parameters.