Journal of Applied Mathematics and Stochastic Analysis
Volume 16 (2003), Issue 1, Pages 33-43
doi:10.1155/S1048953303000030
Abstract
We develop a generalized quasilinearization method for nonlinear initial value problems involving functional differential equations and obtain a sequence of approximate solutions converging monotonically and quadratically to the solution of the problem. In addition, we obtain a monotone sequence of approximate solutions converging uniformly to the solution of the problem, possessing the rate of convergence higher than quadratic.