Journal of Applied Mathematics and Stochastic Analysis 
Volume 7 (1994), Issue 4, Pages 545-552
doi:10.1155/S1048953394000420

Further generalization of generalized quasilinearization method

V. Lakshmikantham1 and N. Shahzad1,2

 1Florida Institute of Technology, Program of Applied Mathematics, Melbourne 32901, FL, USA
2Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
Received 1 June 1994; Revised 1 August 1994

Abstract

The question whether it is possible to develop monotone sequences that converge to the solution quadratically when the function involved in the initial value problem admits a decomposition into a sum of two functions, is answered positively. This extends the method of generalized quasilinearization to a large class.