This paper presents a numerical method for solving the stochastic nonlinear volterra-fredholm integral equation (SNVFIE) driven by a standard Brownian motion (SBM). The method is illustrated via a stochastic operational matrix (SOM) based on the triangular functions (TFs) in combination with the collocation method. With using this approach, the SNVFIE reduces to a stochastic nonlinear system of...

In this paper, we compute piecewise constant bounds on the solution of mixed nonlinear Volterra-Fredholm integral equations. The enclosures are in the form of intervals which are guaranteed to contain the exact solution considering all round-off and truncation errors, so the width of interval solutions allows us to control the error estimation. An iterative algorithm to improve the accuracy of ...

in this paper, the numerical technique based on hybrid bernoulli and block-pulse functions has been developed to approximate the solution of system of linear volterra integral equations. system of volterra integral equations arose in many physical problems such as elastodynamic, quasi-static visco-elasticity and magneto-electro-elastic dynamic problems. these functions are formed by the hybridi...

First, we develop a direct operator method for solving boundary value problems class of nth order linear Volterra–Fredholm integro-differential equations convolution type. The proposed technique is based on the assumption that Volterra bijective and its inverse known in closed form. Existence uniqueness criteria are established exact solution derived. We then apply this to construct form fourth...

In this paper, to solve a linear one-dimensional Volterra  integral equation of the second kind. For this purpose using the equation form, we have defined a linear transformation and by using it's conjugate and reproducing kernel functions, we obtain a basis for the functions space.Then we obtain the solution of  integral equation in terms of the basis functions. The examples presented in this ...

A numerical algorithm, based on a decomposition technique, is presented for solving a class of nonlinear integral equations. The scheme is shown to be highly accurate, and only few terms are required to obtain accurate computable solutions. 1. Introduction. Adomian polynomial algorithm has been extensively used to solve linear and nonlinear problems arising in many interesting applications (see...

This paper presents a numerical expansion-iterative method for solving linear Volterra and Fredholm integral equations of the second kind. The method is based on vector forms of block-pulse functions and their operational matrix. By using this approach, solving the second kind integral equation reduces to solve a recurrence relation. The approximate solution is most easily produced iteratively ...

the spline collocation method  is employed to solve a system of linear and nonlinear fredholm and volterra integro-differential equations. the solutions are collocated by cubic b-spline and the integrand is approximated by the newton-cotes formula. we obtain the unique solution for linear and nonlinear system $(nn+3n)times(nn+3n)$ of integro-differential equations. this approximation reduces th...

Degenerate kernel approximation method is generalized to solve Hammerstein system of Fredholm integral equations of the second kind. This method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. Convergence analysis is investigated and on some test problems, the propo...