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

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.