The method of quasilinearization and a three-point boundary value problem

Abstract

The method of quasilinearization generates a monotone iterationscheme whose iterates converge quadratically to a unique solutionof the problem at hand. In this paper, we apply the method to twofamilies of three-point boundary value problems for second orderordinary differential equations: Linear boundary conditions andnonlinear boundary conditions are addressed independently. Forlinear boundary conditions, an appropriate Green's function isconstructed. For nonlinear boundary conditions, we show thatthese nonlinearities can be addressed similarly to thenonlinearities in the differential equation.