Picard and Adomian methods for quadratic integral equation

Abstract

Mathematical subject classification: Primary: 39B82; Secondary: 44B20, 46C05.

Exact Solutions for a Class of Nonlinear Singular Two-Point Boundary Value Problems: The Decomposition Method

“…The numerical solutions of this nonlinear singular boundary value problem have been discussed by ElSayed [15] and also by Inc and Evans [16]. In [15] the author established three iterative techniques to obtain the numerical solutions.…”

“…In [15] the author established three iterative techniques to obtain the numerical solutions. While in [16], Inc and Evans used the standard ADM with Padé transformation to approximate the solution.…”

“…This singular BVP has been also discussed by ElSayed [15] by using the same iterative techniques to obtain the numerical solutions. Using algorithm (11) for this nonlinear singular boundary value problem, the solution can be elegantly computed by using the recursive scheme…”

“…The numerical results for the absolute errors obtained via integral method [15] and |y(x) − Φ 10 (x)| are shown in Table 2. Here, the approximate solution Φ 10 = ∑ 10 n=0 y n is obtained via algorithm (24).…”

On Numerical Treatment for Volterra - Nonlinear QuadraticIntegral Equation in Two-Dimensions

“…Some numerical and analytical methods can be applied to estimate the solutions of the quadratic integral equations. However, ADM is the most common method used to obtain numerical solutions for quadratic integral equations, [22]- [27], beside some other usefulnumerical methods, [28] and [34].…”