### 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