摘要
研究了一类带有初始弱正则性的时间分数阶对流方程的高精度数值逼近方法,其中时间分数阶导数是Caputo意义上的。结合时间分数阶导数的非均匀Alikhanov公式和空间方向上的间断伽辽金有限元方法给出了全离散数值格式,并分析了格式的稳定性、收敛性和误差估计。最后,通过数值算例验证了算法的有效性和理论精度。
A high-order numerical approximation method of a class of time fractional convection equation with initial weak regularity is studied, where the time fractional derivative is in the Caputo sense.Combined with non-uniform Alikhanov formula of time fractional derivative and discontinuous Galerkin finite element method in spatial direction, a fully discrete numerical scheme is given, and its stability, convergence and error estimate are analyzed. Finally, a numerical example is presented to verify the effectiveness and theoretical accuracy of the algorithm.
作者
王震
WANG Zhen(School of Mathematical Sciences,Jiangsu University,Zhenjiang 212013,China)
出处
《重庆理工大学学报（自然科学）》
CAS
北大核心
2022年第9期253-259,共7页
Journal of Chongqing University of Technology：Natural Science
基金
国家自然科学基金项目(12101266)。
