Efficient inequality-preserving integrators for differential equations satisfying forward Euler condition
数学专题报告
报告题目(Title)：Efficient inequality-preserving integrators for differential equations satisfying forward Euler condition
报告人(Speaker)：张弘（国防科技大学）
地点(Place)：后主楼1124
时间(Time)：2023年8月21日（周一）下午 3:30-4:30
邀请人(Inviter)：张争茹
报告摘要
Developing explicit, high-order accurate, and stable algorithms for nonlinear differential equations remains an exceedingly difficult task. In this work, a systematic approach is proposed to develop high-order schemes that can unconditionally preserve inequality structures shared by a class of differential equations satisfying forward Euler conditions. Strong-stability-preserving (SSP) methods are popular and effective for solving equations of this type. However, few methods can deal with the situation when the time-step size is larger than that allowed by SSP methods. By adopting time-step-dependent stabilization and taking advantage of integrating factor methods in the Shu-Osher form, we propose enforcing the inequality structure preservation by approximating the exponential function using recursive approximations without harming the convergence. The only free parameter can be determined a priori based on the SSP coefficient, the time-step size, and the forward Euler condition. Numerical experiments reflect the high-order accuracy, efficiency, and inequality-preserving properties of the proposed schemes.
主讲人简介
张弘，国防科技大学数学系副教授，硕士生导师。2012年毕业于浙江大学数学系，2014年获国防科大硕士学位，2018年获荷兰乌特勒支大学数学博士学位。主要从事微分方程保结构算法、自适应移动网格方法的研究。在CSIAM Trans Appl. Math, CMAME，JSC，JCP，等期刊发表论文20余篇，入选国防科技大学高层次创新人才,湖南省青年科技人才工程。多次在国际会议（ICOSAHOM 2018/2021, BIRS 2018, HYP 2016等）上进行学术报告。主持国家自然科学基金面上、青年项目等。
