TY - JOUR
T1 - Discretization principles for linear two-point boundary value problems, III
AU - Yamamoto, Tetsuro
AU - Oishi, Shin'Ichi
AU - Nashed, M. Zuhair
AU - Li, Zi Cai
AU - Fang, Qing
N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2008/9
Y1 - 2008/9
N2 - This paper extends results of Yamamoto et al. (Numer. Funct. Anal. Optimiz. 2008; 29:213-224) to the boundary value problem [image omitted] where the sign of r(x) is indefinite. Let HνAνUν= fν be the finite difference equations on partitions [image omitted], =1,2, with [image omitted] as , where Hν and A ν are diagonal and tridiagonal matrices, respectively, and f ν are vectors generated by discretization of f(x). Then equivalent conditions for the boundary value problem to have a unique solution u ∈ C2[a, b] are given in terms of [image omitted] and [image omitted].
AB - This paper extends results of Yamamoto et al. (Numer. Funct. Anal. Optimiz. 2008; 29:213-224) to the boundary value problem [image omitted] where the sign of r(x) is indefinite. Let HνAνUν= fν be the finite difference equations on partitions [image omitted], =1,2, with [image omitted] as , where Hν and A ν are diagonal and tridiagonal matrices, respectively, and f ν are vectors generated by discretization of f(x). Then equivalent conditions for the boundary value problem to have a unique solution u ∈ C2[a, b] are given in terms of [image omitted] and [image omitted].
KW - Discretization principles
KW - Finite difference methods
KW - Two-point boundary value problems
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U2 - 10.1080/01630560802418367
DO - 10.1080/01630560802418367
M3 - Article
AN - SCOPUS:56349102291
SN - 0163-0563
VL - 29
SP - 1180
EP - 1200
JO - Numerical Functional Analysis and Optimization
JF - Numerical Functional Analysis and Optimization
IS - 9-10
ER -