Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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MONOTONE ITERATION SCHEME FOR IMPULSIVE THREE-POINT NONLINEAR BOUNDARY VALUE PROBLEMS WITH QUADRATIC CONVERGENCE

  • Ahmad, Bashir (Department of Mathematics Faculty of Science King Abdulaziz University) ;
  • Alsaedi, Ahmed (Department of Mathematics Faculty of Science King Abdulaziz University) ;
  • Garout, Doa'a (Department of Mathematics Faculty of Science King Abdulaziz University)
  • Published : 2008.09.30
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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.

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References

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