Journal of Applied Mathematics and Stochastic Analysis
Volume 16 (2003), Issue 1, Pages 33-43
doi:10.1155/S1048953303000030

Generalized quasilinearization method for nonlinear functional differential equations

Bashir Ahmad,1 Rehmat Ali Khan,1 and S. Sivasundaram2

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.

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.