郑州大学学报（理学版）2024，Vol.56Issue(2)：87-94,8.DOI:10.13705/j.issn.1671-6841.2022326
分数阶Logistic模型的差分解与环境容纳量反演
Finite Difference Solution for a Fractional-order Logistic Model and Inversion of Carrying Capacity
摘要
Abstract
The problem of a nonlinear fractional-order Logistic model with space-dependent carrying ca-pacity was solved.A finite difference scheme for the forward problem was established,and its stability and convergence were proved based on the estimate of the spectral radius of the coefficient matrix with large capacities.An inverse problem of reconstructing the capacity function with additional measurements at one interior point was solved by the homotopy regularization algorithm,and numerical inversions with noisy data were presented to demonstrate the efficiency of the numerical method.关键词
分数阶Logistic模型/环境容纳量/有限差分格式/稳定性与收敛性/反问题/数值反演Key words
fractional-order Logistic model/carrying capacity of the environment/finite difference solu-tion/stability and convergence/inverse problem/numerical inversion分类
数理科学引用本文复制引用
李怡璇,贾现正,李功胜..分数阶Logistic模型的差分解与环境容纳量反演[J].郑州大学学报（理学版）,2024,56(2):87-94,8.基金项目
国家自然科学基金项目(11871313) （11871313）
山东省自然科学基金项目(ZR2019MA021). （ZR2019MA021）
