Generalized Quasilinearization Method and Cubical Convergence for Mixed Boundary Value Problems

Ramzi S. N. Alsaedi

Abstract

The generalized quasilinearization method for a non-linear secondorder ordinary differential equation with mixed boundary conditions has been studied when the forcing function is the sum of two functions without require that any of the two functions involved to be 2-hyperconvex or 2-hyperconcave. Two sequences are developed under suitable conditions which converge to the unique solution of the boundary value problem. Furthermore, the convergence obtain here is of order 3.