The numerical methods are provided for the long-time dynamics Double Sine-Gordon equation (DSGE), while the nonlinearity is characterized by β/εwith small parameter ε\in(0,1] and interaction parameterβ\in(0,+∞). 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. 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。本科与博士均毕业于山东大学，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，主持了包括国家自然科学基金，天元数学交流项目，湖南省面上项目等。