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

Copyright © 1994 Hindawi Publishing Corporation. 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

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.