### Abstract

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(h^{2}) accurate in the maximum norm, making use of the Banach's fixed point principle.

Original language | English |
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Pages (from-to) | 136-140 |

Number of pages | 5 |

Journal | Applied Mathematics E - Notes |

Volume | 13 |

Publication status | Published - 2013 |

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### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

**Maximum norm analysis for nonlinear two-point boundary value problems.** / Boulbrachene, Messaoud; Kharousi, Fatma Al.

Research output: Contribution to journal › Article

*Applied Mathematics E - Notes*, vol. 13, pp. 136-140.

}

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 2) 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 2) accurate in the maximum norm, making use of the Banach's fixed point principle.

UR - http://www.scopus.com/inward/record.url?scp=84887836000&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84887836000&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84887836000

VL - 13

SP - 136

EP - 140

JO - Applied Mathematics E - Notes

JF - Applied Mathematics E - Notes

SN - 1607-2510

ER -