On Approximation and Numerical Solution of Fredholm-Hammerstein Integral Equations Using Multiquadric Quasi-interpolation

Abstract

Nonlinear integral equations are studied in relation to vehicular traffic, biology, the theory of optimal control, economics, etc. In this paper, we use a numerical method for solving nonlinear Fredholm-Hammerstein integral equations by using multiquadric quasiinterpolation method. Multiquadric quasi-interpolation is an useful instrument in approximation theory and its applications.

Iterative schemes for solving the ChandrasekharH-equation using the Bernstein polynomials

“…Notice that, as we can see in [9], the iterative scheme (10) needs,, in general, to perform fewer iterations to approximate the solution with a given tolerance. Thus, in the following section, by applying iterative process (10), we obtain better accuracy in our approach to the solution and with an similar operational cost to the application of iterative scheme (8). We can therefore conclude that the application of iterative scheme (10) is more efficient than the application of iterative scheme (8).…”

“…which uses the same inverse of the derivative operator in the second step. This iterative scheme achieves an efficient acceleration for the convergence of the Newton-type iterative scheme (8), see [9]. Thus, three are our main goals in this work.…”

“…[4,5,14]. In addition, this kind of equations describe a great variety of mathematical and physics phenomena where one can transform any ordinary differential equation of second order with boundary conditions into a Hammerstein integral equation by using the Green's function [8,13]. For this reason, a great variety of analytical solutions and numerical solutions can be found in the literature for discussing these type of equations (see [1,2,3,7]).…”

"Solutions of Split Equality Hammerstein Type Equation Problems in Reflexive Real Banach Spaces"

“…Generally, as Hammerstein type equations are nonlinear, there is no closed way method to solve such type of equations. So, different authors have introduced different approximation methods for solving Hammerstein type equations (see, for instance, [10,12,14,15,16,18,20,21,25,35,36,40]). Chidume and Zegeye [12,15,16] were the first to propose and study iterative processes for approximating the solution of (1.5).…”

Numerical solution of Fredholm-Hammerstein integral equations by using optimal homotopy asymptotic method and homotopy perturbation method

“…Rabbani et al [4] used wavelet basis to approximate the solution of Fredholm-Hammerstein integral equations. Ezzati et al [5] presented Multiquadric Quasi-interpolation for solving nonlinear Fredholm-Hammerstein integral equations. Ordokhani [6] proposed Walsh-Hybrid Functions to solve Fredholm-Hammerstein integral equations.…”