学会旗舰会刊《CSIAM Transactions on Applied Mathematics》2026年第五期上线发行，欢迎查阅
2026年9月，中国工业与应用数学学会旗舰会刊《CSIAM Transactions on Applied Mathematics》（CSIAM-AM）上线发行2026年第五期。
CSIAM-AM于2020年4月正式创刊，是中国工业与应用数学学会与香港GLOBAL SCIENCE PRESS出版社合作出版的英文季刊。由中国工业与应用数学学会理事长、浙江大学求是讲席教授包刚院士担任主编，学会副理事长、北京大学北京国际数学研究中心张磊教授任总编辑。
2024年CSIAM-AM再次被认定为“中国数学领域高质量科技期刊分级目录”应用数学类T1级，2026年最新影响因子（Impact Factor）为1.1。
CSIAM-AM 2026年第五期共7篇文章，论文目录、摘要及作者信息如下：
Jingwei Li, Kun Wang, Lili Ju
Abstract: The convective Allen-Cahn equation generalizes the classical Allen-Cahn equation by introducing an additional convective term associated with a solenoidal velocity field while maintaining the maximum bound principle (MBP). However, developing high-order numerical schemes that are accurate in both time and space and preserve the MBP unconditionally has remained a significant challenge. In this paper, we address this by first defining new auxiliary variables to reformulate the interaction of the velocity field with the phase field. We then transform the convective Allen-Cahn equation into a generalized Fokker-Planck form using an exponential transformation, enabling the development of MBP-preserving linear numerical schemes. Subsequently, we propose first- and second-order in time numerical schemes for the reformulated equations with a second-order quasi-symmetric finite difference discretization in space. In this approach, the auxiliary variables are replaced with known functions related to the velocity field, simplifying the numerical implementation. For the first-order in time scheme, we derive its optimal error estimate and prove its unconditional MBP-preservation. For the second-order in time scheme, we show its MBP-preservation under mild constraints on the mesh and time step sizes. Some numerical experiments in two and three dimensions are also presented to validate the theoretical findings and illustrate the accuracy and efficiency of our proposed schemes.
Zhengguang Liu, Yanrong Zhang, Xiaoli Li
Abstract:The scalar auxiliary variable (SAV)-type methods are very popular techniques for solving various nonlinear dissipative systems. Compared to the semi-implicit method, the baseline SAV method can keep a modified energy dissipation law but doubles the computational cost. The general SAV approach does not add additional computation but needs to solve a semi-implicit solution in advance, which may potentially compromise the accuracy and stability. In this paper, we construct a novel first- and second-order unconditional energy stable and positivity-preserving stabilized SAV (PS-SAV) schemes for and gradient flows. The constructed schemes can reduce nearly half computational cost of the baseline SAV method and preserve its accuracy and stability simultaneously. Meanwhile, the introduced auxiliary variable is always positive while the baseline SAV cannot guarantee this positivity-preserving property. Unconditionally energy dissipation laws are derived for the proposed numerical schemes. In addition we propose an energy optimization technique to optimize the modified energy close to the original energy. Several interesting numerical examples are presented to demonstrate the accuracy and effectiveness of the proposed methods. Finally, we establish a rigorous error analysis of the fully discrete PS-SAV scheme.
Wenyi Wang, Yiwen Lin
Abstract: The Vlasov-Poisson system is widely used in plasma physics and other related fields. In this paper, we study the Vlasov-Poisson system with initial uncertainty in the quasineutral regime. First, we prove the uniform convergence in the Wasserstein distance between the uncertain Vlasov-Poisson systemin the quasineutral regime and its quasineutral limit system with random initial inputs. This is achieved by deriving an upper bound for the Wasserstein distance and rigorously estimating each component of this bound. Furthermore, by defining a new norm with respect to the quasineutral parameter and estimating the distribution function as well as the electric field in this norm using a variable substitution, we establish the random regularity of the solutions in the quasineutral regime. This work develops a novel framework for quantifying the propagation of the initial uncertainty of the Vlasov-Poisson system in the quasineutral regime, providing a theoretical basis for designing high-performance numerical algorithms.
Xiaoru Yi, Junqing Chen
Abstract: In this paper, we propose a gradient-based method to optimize curvilinear masks in optical lithography. The mask pattern is represented by periodic B-spline curves. We apply constrained Delaunay triangulation to discretize the domains circled by the spline curves. Subsequently, we establish an explicit relationship between the integral points and the control points of the boundary spline curve. Based on the relationship, we derive explicit formulas of the gradient of the optimization objective function with respect to the coordinates of the control points. Then we propose an inverse lithography algorithm to optimize the curvilinear mask pattern. Finally, the results of the numerical experiments demonstrate the feasibility and extensive adaptability of our method.
Yipeng Chen, Yicheng Liu, Xiao Wang
Abstract: This paper studies consensus tracking of collective migration models that involve the alignment force gathering agents and the tracking force matching target. Each agent’s dynamics is controlled by the tracking strategy, which establishes a trade-off between the two forces through a convex combination. In order to drive the system to achieve consensus tracking with the maximum instantaneous convergence speed, an optimal control strategy is proposed that the agents whose alignment force is weaker than, or counteracts its tracking force sense only the target, and become leaders, while the others sense only their neighbours, and become followers. Interestingly, there exist some initial frameworks such that the optimal control strategy consists of letting all agents become followers, which is called “inactivation principle” in [Piccoli, Duteil and Scharf, Math. Models Methods Appl. Sci., 26(2), 2016] and means that the leaderless is better than the leader-follower structure for certain conditions. Both asymptotic and finite-time consensus tracking are investigated. Several numerical simulations show the effect of the optimal control strategy.
Jialin Hong, Chuying Huang, Zhihui Liu
Abstract: We provide a new approach to strong error analysis of the spatial-spectral Galerkin and temporal exponential Euler scheme for a family of second-order parabolic stochastic partial differential equations (SPDEs) driven by multiplicative noise. Applying these results to the stochastic advection-diffusion-reaction equation with a gradient term driven by white noise indicates that this scheme achieves optimal strong convergence order exactly 1/2 in space, which removes an infinitesimal factor in the literature, and 1/4 in time. Numerical experiments support our theoretical analysis.
Fengmiao Bian, Ren Liu, Xiaoqun Zhang
Abstract: Deep neural networks (DNNs) have made great progress in various fields. In particular, the quantized neural network is a promising technique for making DNNs compatible with resource-limited devices for memory and computation saving. In this paper, we mainly consider a non-convex minimization model with three blocks to train quantized DNNs and propose a novel stochastic three-block alternating minimization (STAM) algorithm to solve it. We develop a convergence theory for the STAM algorithm and obtain an -stationary point with an optimal convergence rate. Furthermore, we implement our STAM algorithm to train DNNs with relaxed binary weights. The experiments are carried out on three different network structures, namely VGG-11, VGG-16, and ResNet-18. These DNNs are trained using two different datasets, CIFAR-10 and CIFAR-100, respectively. We compare our STAM algorithm with state-of-the-art algorithms for training quantized neural networks. The test accuracy indicates the effectiveness of our model and algorithm for training relaxed binary quantization DNNs.
期刊官网：https://global-sci.org/index.php/csiam-am。
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