Iterative Reproducing Kernel Method for Solving Second-Order Integrodifferential Equations of Fredholm Type

Abstract

We present an efficient iterative method for solving a class of nonlinear second-order Fredholm integrodifferential equations associated with different boundary conditions. A simple algorithm is given to obtain the approximate solutions for this type of equations based on the reproducing kernel space method. The solution obtained by the method takes form of a convergent series with easily computable components. Furthermore, the error of the approximate solution is monotone decreasing with the increasing of nodal points. The reliability and efficiency of the proposed algorithm are demonstrated by some numerical experiments.

Application of Reproducing Kernel Hilbert Space Method for Solving a Class of Nonlinear Integral Equations

“…The mentioned scheme above is an efficient method of solving nonlinear equations [31][32][33]. However, in implementing this algorithm on a computer, { ( )} ∞ =1 is not quite orthogonal, due to rounding errors.…”

On the solutions of electrohydrodynamic flow with fractional differential equations by reproducing kernel method

“…Many problems such as population models and complex dynamics have been solved in the reproducing kernel spaces [7,17,26,27]. For more details of this method see [1,2,5,8,15,16,19,25,28,29].…”

Approximate Series Solution of Nonlinear, Fractional Klein-Gordon Equations Using Fractional Reduced Differential Transform Method

“…For examples of these methods, we refer to the work in (Hesameddini and Fotros, 2012;Moaddy et al, 2011;Abdulaziz et al, 2008;Hashim et al, 2009;Odibat and Momani, 2006;Khalil et al, 2015a;2015b;2015c;El-Ajou et al, 2015;Abu-Gdairi et al, 2015;Freihat and Al-Smadi, 2013;Momani et al, 2014;Al-Smadi et al, 2013;. On the other hand, many applications for different problems by using other numerical algorithms can be found in (Abu Arqub et al, 2012;Abu Arqub and Al-Smadi, 2014;Moaddy et al, 2015;Komashynska and Al-Smadi, 2014;Komashynska et al, 2016).…”