Journal of Applied Mathematics and Stochastic Analysis
Volume 16 (2003), Issue 1, Pages 33-43
Generalized quasilinearization method for nonlinear functional
1Quaid-i-Azam University, Department of Mathematics, Islamabad, Pakistan
2Embry-Riddle Aeronautical University, Department of Mathematics, Daytona Beach 32114, FL, USA
Received 1 March 2002; Revised 1 October 2002
Copyright © 2003 Bashir Ahmad et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.