TY - JOUR
T1 - Maximum norm analysis for nonlinear two-point boundary value problems
AU - Boulbrachene, Messaoud
AU - Kharousi, Fatma Al
PY - 2013
Y1 - 2013
N2 - In this paper, we propose a new approach for the finite difference approxi- mation on non-uniform mesh of the nonlinear two-point boundary value problem-(p(x)u')' = f(x, u); a < x < b; u(a) = u(b) = 0. Under a realistic assump-tion on the nonlinearity and a C3;1[a; b] regularity of the solution, we show that the approximation is O(h2) accurate in the maximum norm, making use of the Banach's fixed point principle.
AB - In this paper, we propose a new approach for the finite difference approxi- mation on non-uniform mesh of the nonlinear two-point boundary value problem-(p(x)u')' = f(x, u); a < x < b; u(a) = u(b) = 0. Under a realistic assump-tion on the nonlinearity and a C3;1[a; b] regularity of the solution, we show that the approximation is O(h2) accurate in the maximum norm, making use of the Banach's fixed point principle.
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M3 - Article
AN - SCOPUS:84887836000
SN - 1607-2510
VL - 13
SP - 136
EP - 140
JO - Applied Mathematics E - Notes
JF - Applied Mathematics E - Notes
ER -