A FINITE POINT METHOD BASED ON DIRECTIONAL DIFFERENCES

作者：Shen Longjun^*; Lv Guixia; Shen Zhijun

来源：SIAM Journal on Numerical Analysis, 2009, 47(3): 2224-2242.

DOI：10.1137/08072200X

• finite point method
• directional differential
• directional difference
• five-point formulae
• solvability conditions
• permissible neighboring point set

A new approach to the finite point method (FPM) on scattered points in two space dimensions is presented which is based on the directional differential and directional difference. The relations between the multidirectional differentials of each order are derived. Based on these relations, some explicit five-point formulae are obtained for second-order accurate approximation of the first-order directional derivatives and for first-order accurate approximation of the second-order directional derivatives. Solvability conditions for the five-point formulae and the methods for selecting the permissible neighboring point set are discussed. Numerical experiments are presented to demonstrate the performance and convergence of the proposed method.

• 出版日期2009