应用数学2025，Vol.38Issue(2)：595-606,12.
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
摘要
Abstract
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 Crank-Nicholson 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Key words
Squirrel search algorithm/Reaction-diffusion equation/Inverse problem/The barycen-tric form of interpolation/Singularly perturbed分类
数学引用本文复制引用
麦雄发,卞文贺,刘利斌,毛志..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[J].应用数学,2025,38(2):595-606,12.基金项目
广西科技计划项目(桂科AD23023003) （桂科AD23023003）
国家自然科学基金(12361087) （12361087）
