An iterative method for solving nonlinear functional equations

Abstract

An iterative method for solving nonlinear functional equations, viz. nonlinear Volterra integral equations, algebraic equations and systems of ordinary differential equation, nonlinear algebraic equations and fractional differential equations has been discussed.  2005 Elsevier Inc. All rights reserved.

Iterative methods for solving scalar equations

“…Many iterative methods involving various techniques have been established to find the approximate roots of nonlinear equations, see [1,3,4,5,7,10,11,13] and references there in. These methods can be classified as one-step, two-step and three-step methods.…”

“…Having motivation from the recent research, we establish new iterative methods for finding multiple roots of scalar equations by using decomposition techniques due to Daftardar-Gejji and Jafari [10].…”

On Approximate Solution Of Fractional Order Logistic Equations By Operational Matrices Of Bernstein Polynomials

“…In the literature we see some papers on the study of FOLE including [20] by El-Sayed et al In [19] S. Bhalekar and V. D. Gejji considered FOLE by the new iterative method introduced by D. Gejji and H. Jafari in [21].…”

Solution of fractional partial differential equations using iterative method

“…Transport phenomena is governed by fractional transport equations. These types of equations are solved by various methods such as Adomain decomposition method [1], [2], [11], [13], [22], homotopy perturbation method [18], [19], [20], [30], variational iteration method [17], [21], an iterative method [4], [6], [8], [9], [12], finite element method [14], finite difference method [16], finite sine transform method [3], method of images and Fourier transform [27], as well as Green's function method [34].…”

“…Now we discuss the iterative method developed by Daftardar-Gejji and Jafari in [8]. It is also called new iterative method.…”