带有广义记忆核Caputo分数阶导数的一种新数值离散格式  

A New Numerical Discrete Scheme of Caputo Fractional Derivative with Generalized Memory Kernel

作　　者：胡小兰 梁宗旗[1] HU Xiaolan;LIANG Zongqi(School of Science,Jimei University,Xiamen 361021,China)

机构地区：[1]集美大学理学院,福建厦门361021

出　　处：《集美大学学报(自然科学版)》2025年第1期88-94,共7页Journal of Jimei University:Natural Science

基　　金：国家自然科学基金项目“棱柱错位环自攀移的数值模拟和相场模型”(11801214);福建省自然科学基金项目“基于深度过完备字典的大倍数超分辨率重建研究”(2020J01710);福建省自然科学基金项目“非局部问题及反常扩散方程最优控制问题的数值方法”(2020J01703)。

摘　　要：本文主要研究了带有广义记忆核Caputo型分数阶导数的L_(1)差分格式。利用L_(1)线性插值和降阶法构造了带有广义记忆核α(1<α<2)阶Caputo型分数阶导数的离散格式,研究了其系数性质,并给出了其截断误差,收敛阶为O(τ^(3-α))。最后,通过数值算例验证了该格式的有效性和数值精度。The L_(1) difference scheme of Caputo-fractional derivative with the generalized memory kernel is proposed in this paper.By the linear interpolation and reduced order method,the discrete numerical scheme of Caputo-fractional derivative with the generalized memory kernelα(1<α<2),namely L_(1) numerical scheme,is presented,and the nature of the coefficients is also proved.Additionally,an error estimate of numerical scheme is provided,demonstrating that the convergence order is O(τ^(3-α)),whereτandα∈(1,2)are the time step size and the fractional order,respectively.The numerical example is presented to demonstrate the effectiveness of the proposed method and the numerical accuracy is validated.

关 键 词：CAPUTO分数阶导数 L_(1)插值 降阶法 收敛阶 

分 类 号：O241.82[理学—计算数学]