THEORETICAL ANALYSES ON DISCRETE FORMULAE OF DIRECTIONAL DIFFERENTIALS IN THE FINITE POINT METHOD  

作　　者：Guixia Lv Longjun Shen 

机构地区：[1]Laboratory of Computational Physics,Institute of Applied Physics and Computational Mathematics,P.0.Box 8009-26,Beijing 100088,China

出　　处：《Journal of Computational Mathematics》2022年第1期1-25,共25页计算数学（英文）

基　　金：supported by the National Natural Science Foundation of China(11671049);the Foundation of LCP,and the CAEP Foundation(CX2019026).

摘　　要：For the five-point discrete formulae of directional derivatives in the finite point method,overcoming the challenge resulted from scattered point sets and making full use of the explicit expressions and accuracy of the formulae,this paper obtains a number of theoretical results:(1)a concise expression with definite meaning of the complicated directional difference coefficient matrix is presented,which characterizes the correlation between coefficients and the connection between coefficients and scattered geometric characteristics;(2)various expressions of the discriminant function for the solvability of numerical differentials along with the estimation of its lower bound are given,which are the bases for selecting neighboring points and making analysis;(3)the estimations of combinatorial elements and of each element in the directional difference coefficient matrix are put out,which exclude the existence of singularity.Finally,the theoretical analysis results are verified by numerical calculations.The results of this paper have strong regularity,which lay the foundation for further research on the finite point method for solving partial differential equations.

关 键 词：Finite point method Finite difference Scattered point distribution Discrete directional differentials Theoretical analysis 

分 类 号：O17[理学—数学]