数学
类型(生物学)
数值积分
领域(数学分析)
应用数学
偏微分方程
订单(交换)
数学分析
财务
经济
生态学
生物
作者
Min Lei,Pengyuan Liu,Y.C. Hon
标识
DOI:10.1016/j.enganabound.2023.04.012
摘要
In this paper, we combine the finite integration method (FIM) with the technique of fictitious points to solve high order partial differential equations (HOPDEs). Two type of fictitious finite integration method (FFIM) are proposed and analyzed. The first type FFIM (FFIM-I) constructs the first order integration matrices by shifted Chebyshev polynomials so that the analytical high order integration matrices can be recursively obtained. Compared with the classical FIM, whose high order integration matrices are approximated directly through low order integration matrices, this FFIM-I leads to higher accuracy. Based on FFIM-I, the second type FFIM (FFIM-II) is proposed in which the fictitious points are located freely either inside or outside the problem domain. The FFIM-II can further improve the performance of FFIM-I in solving HOPDEs. The advantage of this fictitious finite integration method will be demonstrated by making comparisons among FIM, FFIM-I and FFIM-II through several 2D and 3D numerical experiments.
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