IJPAM: Volume 41, No. 6 (2007)

ACCURACY OF THIRD-ORDER FINITE DIFFERENCE
SCHEMES FOR SECOND DERIVATIVE APPROXIMATION
ON NON-UNIFORM GRIDS

Zhang Kun$^1$, Wang Liangbi$^2$, Chang Yingxiang$^3$
$^{1,2,3}$School of Mathematics
Lanzhou Jiaotong University
Lanzhou, 730070, P.R. CHINA
$^1$e-mail: zhangkun52015@sohu.com
$^2$e-mail: lbwang@lzjtu.cn


Abstract.The Fourier error analysis of classical and compact differencing errors with third order accuracy for second derivative approximation on non-uniform grid system are presented. The results show that for uniform mesh compact difference scheme is superior to classical difference scheme, but for non-uniform the grid quality has stronger effects on compact scheme than on the classical scheme.

Received: July 20, 2007

AMS Subject Classification: 65D25, 65F22

Key Words and Phrases: Fourier analysis, classical difference scheme, compact difference scheme, second derivative approximation, third order accuracy, non-uniform mesh

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 41
Issue: 6