THE METHOD OF QUASILINEARIZATION AND A THREE-POINT BOUNDARY VALUE PROBLEM Eloe, Paul W.; Gao, Yang;
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.
quasilincarization;quadratic convergence;boundary value problem;nonlinear boundary condition;
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