基于改进松鼠搜索算法的奇异摄动反应扩散方程系数反演问题  

An Improved Squirrel Search Algorithm for a Coefficient Inversion Problem of a Singularly Perturbed Reaction-diffusion Equation

作　　者：麦雄发 卞文贺 刘利斌 毛志 MAI Xiongfa;BIAN Wenhe;LIU Libin;MAO Zhi(Center for Applied Mathematics of Guangxi,Nanning Normal University,Nanning 530100,China;School of Data Science,Tongren University,Tongren 554300,China)

机构地区：[1]南宁师范大学广西应用数学中心,广西南宁530100 [2]铜仁学院大数据学院,贵州铜仁554300

出　　处：《应用数学》2025年第2期595-606,共12页Mathematica Applicata

基　　金：广西科技计划项目(桂科AD23023003);国家自然科学基金(12361087)。

摘　　要：本文提出一种新的数值算法,用于求解具有最终时间观测数据的奇异摄动反应扩散方程系数反演问题.对于正问题的数值离散,本文使用基于sinh变换的重心有理插值对空间导数进行离散,并使用Crank-Nicholson有限差分对时间导数进行近似.然后,将此反问题转换为一个最小化问题.为求解此最小化问题,本文通过结合最优邻域搜索策略、随机对立学习策略和自适应捕食者存在概率策略,提出了一种改进的松鼠搜索算法——NOISSA.最后,本文进行了一系列数值实验,以此说明本文提出的新算法在解决奇异摄动反应扩散方程系数反演问题方面的优势.This paper introduces a novel numerical algorithm to solve the inverse problem of a coefficient inversion for a singularly perturbed reaction-diffusion equations with final-time observation data.For the numerical discretization of the forward problem,this paper employs a barycentric rational interpolation based on the sinh transformation to discretize the spatial derivatives and uses the CrankNicholson finite difference method to approximate the temporal derivatives.Subsequently,the inverse problem is transformed into a minimization problem.To solve this minimization problem,an improved squirrel search algorithm,named NOISSA,is proposed by combining an optimal neighborhood search strategy,a random opposition-based learning strategy,and an adaptive predator existence probability strategy.Finally,a series of numerical experiments are conducted to demonstrate the advantages of the new algorithm proposed in this paper in solving the coefficient inverse problem for the singularly perturbed reaction-diffusion equation.

关 键 词：松鼠搜索算法 反应扩散方程 反问题 重心有理插值 奇异摄动 

分 类 号：O241[理学—计算数学]