关于非线性常微分方程组中平均变量近似动力学的计算方法：走向速率型本构方程的推导

优化大型ODE系统去卷积模型降阶的性能

Optimizing performance of the deconvolution model reduction for large ODE systems

本文通过截断奇异值分解（SVD）正则化方法，研究去卷积闭包在Irwing-Kirkwood-Noll过程中的数值性能，分析各参数对精度和效率的影响。

Geometric integration of ODEs using multiple quadratic auxiliary variables

We present a novel numerical method for solving ODEs while preserving polynomial first integrals. The method is based on introducing multiple quadratic auxiliary variables to reformulate the ODE as an equivalent but higher-dimensional ODE with only quadratic integrals to which the midpoint rule is applied. The quadratic auxiliary variables can subsequently be eliminated yielding a midpoint-like method on the original phase space. The resulting method is shown to be a novel discrete gradient method. Furthermore, the averaged vector field method can be obtained as a special case of the proposed …

Global Controllability for Quasilinear Non-negative Definite System of ODEs and SDEs

We consider exact and averaged control problem for a system of quasi-linear ODEs and SDEs with a non-negative definite symmetric matrix of the system. The strategy of the proof is the standard linearization of the system by fixing the function appearing in the nonlinear part of the system, and then applying the Leray-Schauder fixed point theorem. We shall also need the continuous induction arguments to prolong the control to the final state which is a novel approach in the field. This enables us to obtain controllability for arbitrarily large initial data (so called global controllability).

用于任意完全电和磁各向异性Maxwell方程的稳定3D FDTD方法

Stable 3D FDTD Method for arbitrary Fully Electric and Magnetic Anisotropic Maxwell Equations

本文提出了一种新的3D FDTD Maxwell求解器，用于任意电和磁各向异性介质，采用非平均和平均方法，前者为一阶精度，后者为二阶精度。通过数学证明和数值测试验证了方法的稳定性与准确性，展示了在复杂介质中的应用效果。

加权本质非振荡方案的皮卡德积分公式

The Picard integral formulation of weighted essentially non-oscillatory schemes

本文提出基于修正通量方法的皮卡德积分公式，用于推导新的泰勒和龙格-库塔方法，通过WENO重构构建守恒有限差分方法，实现自动守恒性，适用于一维和二维的超保守律问题。

Higher order phase averaging for highly oscillatory systems

We introduce a higher order phase averaging method for nonlinear oscillatory systems. Phase averaging is a technique to filter fast motions from the dynamics whilst still accounting for their effect on the slow dynamics. Phase averaging is useful for deriving reduced models that can be solved numerically with more efficiency, since larger timesteps can be taken. Recently, Haut and Wingate (2014) introduced the idea of computing finite window numerical phase averages in parallel as the basis for a coarse propagator for a parallel-in-time algorithm. In this contribution, we provide a framework f…