Differential inequalities and their application to a convergence proof of quasilinearization

Abstract

Theorems concerned with differential inequalities are developed. These are then used to derive upper bounds on the norms of solutions to systems of second-order, linear differential equations and on the norms of solutions to associated two-point boundary-value problems. The theory is applied to a new convergence theorem for quasilinearization, an important method for the solution of two-point boundary-value problems associated with nonlinear differential equations.