There are several classifications of linear Integral Equations. Some them include; Voltera Equations, Fredholm Linear Fredholm-Voltera Integrodifferential. In the past, solutions higher-order Fredholm-Volterra Integrodifferential Equations [FVIE] have been presented. However, this work uses a computational techniques premised on third kind Chebyshev polynomials method. The performance results f...

In this paper a numerical technique is presented for the solution of fuzzy linear Volterra-Fredholm-Hammerstein integral equations. This method is a combination of collocation method and radial basis functions(RBFs).We first solve the actual set are equivalent to the fuzzy set, then answer 1-cut into the equation. Also high convergence rates and good accuracy are obtain with the propose method ...

In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...

*Correspondence: [email protected] School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, P.R. China Abstract In this paper, we study some new retarded Volterra-Fredholm type integral inequalities on time scales, which provide explicit bounds on unknown functions. These inequalities generalize and extend some known inequalities and can be used as tools in the qualitative theory ...

In this paper, we present a numerical method to solve the nonlinear Volterra-Fredholm integral equations by new basis functions (NFs). This is demonstrated by using a complementary pair of new orthogonal basis functions set (NFs) derived from the well-known block pulse functions set. Finally, we give some numerical examples, and the efficiency of this method will be shown by comparison with som...

In this paper, we propose a new numerical method for solution of Urysohn two dimensional mixed Volterra-Fredholm integral equations of the second kind on a non-rectangular domain. The method approximates the solution by the discrete collocation method based on inverse multiquadric radial basis functions (RBFs) constructed on a set of disordered data. The method is a meshless method, because it ...

A numerical method based on modified block pulse functions is proposed for solving the mixed linear Volterra-Fredholm integral equations. We obtain an integration operational matrix of interval [0,T). and their integration, equations can be reduced to a system algebraic The rate convergence O(h) error analysis are discussed. Some examples provided show that have good degree accuracy.

In this paper, a numerical procedure for solving a class of nonlinear VolterraFredholm integral equations is presented. The method is based upon the globally defined sinc basis functions. Properties of the sinc procedure are utilized to reduce the computation of the nonlinear integral equations to some algebraic equations. Illustrative examples are included to demonstrate the validity and appli...

We propose a new method, called the textit{the weighted space method}, for the study of the generalized Hyers-Ulam-Rassias stability. We use this method for a nonlinear functional equation, for Volterra and Fredholm integral operators.