Approximate Solution of Urysohn Integral Equations Using the Adomian Decomposition Method

Abstract

We apply Adomian decomposition method (ADM) for obtaining approximate series solution of Urysohn integral equations. The ADM provides a direct recursive scheme for solving such problems approximately. The approximations of the solution are obtained in the form of series with easily calculable components. Furthermore, we also discuss the convergence and error analysis of the ADM. Moreover, three numerical examples are included to demonstrate the accuracy and applicability of the method.

A numerical method for solving Urysohn type integral equations

“…In this section, we apply the proposed method to solve some examples. The results obtained by proposed method are compared with other existing methods used in [13,14]. The absolute errors are given by .…”

“…Equating the terms whit identical power of , p we obtain Comparison between the absolute error for the solution of Eq. (13) for the present method and those methods used in [13,14] is presented in Table 2. The plot of results Eq.…”

“…Many different semi-analytical methods have been applied for solving Urysohn integral equations in mathematics, physics, mechanics and engineering. In [14], Singh et al studied the approximate solution to Urysohn integral equations by Adomian decomposition method. In [13], Nadjafi and Heidari used…”

“…Let's first consider nonlinear Urysohn integral equation[13,14] For solving this example by the HPM, we choose a convex homotopy…”

A Novel Approach for the Solution of a Class of Urysohn Integrale Quations Using Bernstein Polynomials.

“…The Adomian decomposition method (ADM) for obtaining approximate series solution of Urysohn integral equations was presented in [2]. The numerical approximation solution of the Urysohn integralequationwithtwomethodshasbeenworkedout in [3].…”