Generalized quasilinearization method for nonlinear functional differential equations
type: Item
instance of: scholarly article
title: Generalized quasilinearization method for nonlinear functional differential equations
zbMATH Open document ID: 1048.34105
DOI: 10.1155/S1048953303000030
author: Bashir Ahmad
author: Rahmat Ali Khan
author: Seenith Sivasundaram
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 2003-10-07T00:00:00Z
full work available at URL: https://eudml.org/doc/50978
review text: The authors investigate a nonlinear initial value problem for the functional-differential equation \(x'= f(t,x_t)\), \(t\in [0,T]\), with \(x_t(s)= x(s+ t)\), \(-\tau\leq s\leq 0\), \(t\in [-\tau,T]\), \(\tau> 0\), \(f\in C[J\times\Gamma, \mathbb{R}]\) and \(\Gamma= C[[-\tau, 0],\mathbb{R}]\). They develop a method called ``quasilinearization'' for this equation without requiring the function involved to be convex concave. A monotone sequence of approximate solutions converging monotonically to a solution to the problem, with convergence higher then quandratic, is obtained.
Mathematics Subject Classification ID: 34K07
zbMATH DE Number: 1932173
zbMATH Keywords: nonlinear initial value problem
zbMATH Keywords: functional-differential equation
zbMATH Keywords: quasilinearization
reviewed by: Ludvík Janoš
MaRDI profile type: Publication
OpenAlex ID: W2114647093
description: scientific article; zbMATH DE number 1932173