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 -