数学
离散化
交替方向隐式方法
应用数学
趋同(经济学)
正确性
理论(学习稳定性)
空格(标点符号)
有限差分
有限差分法
数学分析
算法
计算机科学
操作系统
机器学习
经济增长
经济
作者
Mingchao Zhao,H.M. Chen,Kexin Li
摘要
Abstract This work develops two temporal second‐order alternating direction implicit (ADI) numerical schemes for solving multidimensional parabolic‐type integrodifferential equations with multi‐term weakly singular Abel kernels. For the two‐dimensional (2D) case, applying the Crank–Nicolson method and product integration rule to discretizations of temporal derivative and integral terms, respectively, and the spatial discretization is proposed using a compact difference formulation combined with the ADI algorithm; for the three‐dimensional case, the method of temporal discretization is the same as the 2D case, and then we employ the standard finite difference in space to construct a fully discrete ADI finite difference scheme. The ADI technique is used to reduce the calculation cost of the high‐dimensional problem. Besides, the stability and convergence of two ADI schemes are rigorously proved by the energy argument, in which the first scheme converges to the order , where , , and denote the time‐space step sizes, respectively, and the second scheme converges to the space‐time second‐order accuracy. Finally, the numerical results verify the correctness of the theoretical analysis and show that the method of this article is competitive with the existing research work.
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