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THE METHOD OF QUASILINEARIZATION AND A THREE-POINT BOUNDARY VALUE PROBLEM

  • Eloe, Paul W. ;
  • Gao, Yang
  • Published : 2002.03.01

Abstract

The method of quasilinearization generates a monotone iteration scheme whose iterates converge quadratically to a unique solution of the problem at hand. In this paper, we apply the method to two families of three-point boundary value problems for second order ordinary differential equations: Linear boundary conditions and nonlinear boundary conditions are addressed independently. For linear boundary conditions, an appropriate Green\`s function is constructed. Fer nonlinear boundary conditions, we show that these nonlinearities can be addressed similarly to the nonlinearities in the differential equation.

Keywords

quasilincarization;quadratic convergence;boundary value problem;nonlinear boundary condition

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