报告人：宋怀玲（湖南大学）

报告时间：2026年5月7日（星期四）15:00-17:30

报告地点：科技楼南楼706室

报告摘要：The numerical methods are provided for the nonlinear Double Sine-Gordon equation (DSGE), while the nonlinearity is characterized by $\beta/\epsilon$ with small parameter $\epsilon\in(0,1]$ and interaction parameter $\beta\in(0,+\infty)$. In comparison to the Sine-Gordon equation, DSGE has many properties of solitons as well as its own unique new features. In this talk, a family of novel energy-preserving schemes are presented for numerically solving the DSGE. These schemes are constructed by using an auxiliary variable in the integrating factor Runge-Kutta (IFRK) method. In virtue of the auxiliary variable, the proposed method is high-order accurate, preserves the original discrete energy through the solution of only one scalar equation per time step, while the previous energy-preserving schemes for long-time dynamics are usually implicit. Meanwhile, the improved uniform error bounds are proved. We further extend these bounds to two oscillatory DSGEs with O(ε^2) and O(ε^2/β^2) wavelength in time. Numerical experiments demonstrate that our schemes exhibit superior long-time energy conservation and accuracy, with excellent performance in simulating the solitons dynamics of both DSG and SG equations.

报告人简介：宋怀玲，湖南大学数学学院教授，博士生导师，从事数学理论、计算方法和高效数值算法的教学和科研工作。博士毕业于山东大学，主要研究兴趣包括相场模型、相场耦合模型、非局部模型和多孔介质两相流问题的高阶数值方法的建立以及模型约化与应用等。相关研究成果发表在Computer Methods in Applied Mechanics and Engineering、Journal of Computational Physics、Journal of Scientific computing、Communications in Computational Physics等计算数学国际期刊。

邀请人：李东方