An Extension of the Generalized Quasilinearization Method of Lakshmikantham

Abstract

We extend the generalized quasilinearization method of Lakshmikantham for an initial value problem for an ordinary differential equation to the case of a sum of two right hand functions. The first member will satisfy a convexity condition proposed by Lakshmikantham, while the second member will satisfy a corresponding weaker form of convexity condition. Monotone and quadratic convergence are preserved.