MONOTONE ITERATION SCHEME FOR IMPULSIVE THREE-POINT NONLINEAR BOUNDARY VALUE PROBLEMS WITH QUADRATIC CONVERGENCE

- Journal title : Journal of the Korean Mathematical Society
- Volume 45, Issue 5, 2008, pp.1275-1295
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2008.45.5.1275

Title & Authors

MONOTONE ITERATION SCHEME FOR IMPULSIVE THREE-POINT NONLINEAR BOUNDARY VALUE PROBLEMS WITH QUADRATIC CONVERGENCE

Ahmad, Bashir; Alsaedi, Ahmed; Garout, Doa`a;

Ahmad, Bashir; Alsaedi, Ahmed; Garout, Doa`a;

Abstract

In this paper, we consider an impulsive nonlinear second order ordinary differential equation with nonlinear three-point boundary conditions and develop a monotone iteration scheme by relaxing the convexity assumption on the function involved in the differential equation and the concavity assumption on nonlinearities in the boundary conditions. In fact, we obtain monotone sequences of iterates (approximate solutions) converging quadratically to the unique solution of the impulsive three-point boundary value problem.

Keywords

quasilinearization;three-point boundary value problems; quadratic convergence;

Language

English

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