This article introduces a numerical method based on an M(n+ 1) set of general, hybrid orthonormal Bernstein functions coupled with Block-Pulse Functions(HOBB) on the interval [0,1] for approximating solutions of a Coupled System of linear and non linear Volterra integral and Integro-Differential equations. This method reduces a Coupled System of Volterra integral and IntegroDifferential equatio...

In this paper the fixed point theorem of Schauder is used to prove the existence of a continuous solution of the nonlinear fuzzy Volterra integral equations. Then using some conditions the uniqueness of the solution is investigated.

In this paper, a nonlinear inverse problem of parabolic type, is considered. By reducing this inverse problem to a system of Volterra integral equations the existence, uniqueness, and stability of the solution will be shown.

Algebraic integral equations is a special category of Volterra integral equations system,  that has many applications in physics and engineering. The principal aim of this paper is to serve the numerical solution of an integral algebraic equation by using the Taylor expansion method. In this method, using the Taylor expansion of the unknown function, the algebraic integral equation system becom...

Rationalized Haar functions are developed to approximate the solution of the nonlinear Volterra–Fredholm–Hammerstein integral equations. The properties of rationalized Haar functions are first presented. These properties together with the Newton–Cotes nodes and Newton–Cotes integration method are then utilized to reduce the solution of Volterra–Fredholm–Hammerstein integral equations to the sol...

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear m...

We consider numerical solutions of a class of nonlinear (nonstandard) Volterra integral equations. We first prove the existence and uniqueness of the solution of the Volterra integral equation in the context of the space of continuous funtions over a closed interval. We then use one point collocation methods and quadrature methods with a uniform mesh to construct solutions of the nonlinear VIE....

The main purpose of this article is to demonstrate the use of the two Dimensional Walsh and Haar functions with Operational Matrix for solving nonlinear Volterra-Fredholm integral equations. The approximate solution is represented in the form of series. The approximate solution is obtained by two Dimensional Walsh and Haar series. The operational matrix and direct method for solving the linear ...

Mean-field backward stochastic Volterra integral equations (MF-BSVIEs, for short) are introduced and studied. Well-posedness of MF-BSVIEs in the sense of introduced adapted Msolutions is established. Two duality principles between linear mean-field (forward) stochastic Volterra integral equations (MF-FSVIEs, for short) and MF-BSVIEs are obtained. Several comparison theorems for MF-FSVIEs and MF...

In this work, we present a numerical method for solving nonlinear Fredholmand Volterra integral equations of the second kind which is based on the useof Block Pulse functions(BPfs) and collocation method. Numerical examplesshow eciency of the method.