Alternative Legendre polynomials (ALPs) are used to approximate the solution of a class of nonlinear Volterra-Hammerstein integral equations. For this purpose, the operational matrices of integration and the product for ALPs are derived. Then, using the collocation method, the considered problem is reduced into a set of nonlinear algebraic equations. The error analysis of the method is given an...

There are various numerical methods to solve nonlinear integral equations. Most of them transform the integral equation into a system of nonlinear algebraic equations. It is cumbersome to solve these systems, or the solution may be unreliable. In this paper, we study the application of the fixed point method to solve Volterra-Hammerstein integral equations. This method does not lead to a nonlin...

In this paper, interval Legendre wavelet method is investigated to approximated the solution of the interval Volterra-Fredholm-Hammerstein integral equation. The shifted interval Legendre polynomials are introduced and based on interval Legendre wavelet method is defined. The existence and uniqueness theorem for the interval Volterra-Fredholm-Hammerstein integral equations is proved. Some examp...

In this paper, numerical solution of nonlinear fuzzy Hammerstein integral equations is studied by fuzzy B-spline series. An error bound for the method is found based on modulus of continuity and it is proved that the proposed algorithm is numerically stable. Finally, theoretical results are illustrated by some numerical examples.

Keywords: Functional integral equation Existence Monotonic solutions Urysohn Compact in measure a b s t r a c t We study the existence of monotonic solutions for a perturbed functional integral equation of Urysohn type in the space of Lebesgue integrable functions on an unbounded interval. The technique associated with measures of noncompactness (in both the weak and the strong sense) and the D...