Extended quasilinearization method for periodic boundary value problem of first order delay differential equations

Abstract

n this paper, we discuss the extended quasilinearization method to first order delay differential equation of the type x' (t) + Lambda x(t) = f(t, x(t - r)) + g(t, x(t - r)) with periodic boundary conditions, where there are certain conditions on first and second order partial derivatives with respect to the second coordinate of f and g. The quasilinearization method helps us to find sequence of approximate solutions to non-linear problem, the limit of which, if exists, tends to a solution of the given non-linear problem.