基于再生核和有限差分法求解变系数时间分数阶对流扩散方程  

Combining RKM with FDM for Time Fractional Convection-Diffusion Equations with Variable Coefficients

作　　者：吕学琴 何松岩[3] 王世宇 Xueqin Lv;Songyan He;Shiyu Wang(College of Basic Science,Tianjin Sino-German University of Applied Sciences,Tianjin 300350;School of Mathematics and Sciences,Harbin Normal University,Harbin 150025;School of Mathematics and Statistics,Northeast Normal University,Changchun 130024;Beijing No.101 Middle School Changping Experimental School,Beijing 102206)

机构地区：[1]天津中德应用技术大学基础课部,天津300350 [2]哈尔滨师范大学数学科学学院,哈尔滨150025 [3]东北师范大学数学与统计学院,长春130024 [4]北京市第一〇一中学昌平实验学校,北京102206

出　　处：《数学物理学报(A辑)》2025年第1期153-164,共12页Acta Mathematica Scientia

基　　金：天津市高等教育委员会科技发展基金(2019KJ142);天津中德应用技术大学教学质量与教学改革研究计划项目(A2301)。

摘　　要：针对变系数的时间分数阶对流-扩散方程,首先,使用有限差分法,得到了该方程的半离散格式.之后再利用再生核方法,得到了方程的精确解u(x,t_(n)),将精确解u(x,t_(n))取m项截断,可得到近似解u_(m)(x,t_(n)).通过证明,得到该方法是稳定的.最后,通过三个数值例子,并与其他文献中的方法在同等条件下进行了比较,证明该算法有效.In this paper,we will study the time fractional convection-diffusion equation with variable coefficients.First,we use the finite difference method.The time variable is discretized,and the semi-discrete scheme of the equation is obtained.The exact solution u(x,t_(n))of the equation is obtained by using the theory of reproducing kernel method.Then the exact solution u(x,t_(n))is truncated by m term to obtain the approximate solution u_(m)(x,t_(n)).By proving,we know that the method is stable.Moreover,u(i)m(x,t_(n))converge uniformly to u(i)(x,t_(n))(i=0,1,2).Finally,we give several numerical examples and compare them with the methods in other literatures,which show that our algorithm is effective.

关 键 词：CAPUTO分数阶导数 再生核方法 变系数时间分数阶对流扩散方程 有限差分方法 

分 类 号：O24[理学—计算数学]