In this study‎, ‎an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials‎. ‎Properties of these polynomials and operational matrix of integration are first presented‎. ‎These properties are then used to transform the integral equation to a matrix equation which corresponds t...

The introduced method in this study consists of reducing a system of infinite boundary integro-differential equations (IBI-DE) into a system of al- gebraic equations, by expanding the unknown functions, as a series in terms of Laguerre polynomials with unknown coefficients. Properties of these polynomials and operational matrix of integration are rst presented. Finally, two examples illustra...

*Correspondence: [email protected] Department of Mathematics and Computer Sciences, Ariel University of Samaria, Ariel, Israel Abstract The purpose of this paper is to propose a method for studying integro-differential equations with infinite limits of integration. The main idea of this method is to reduce integro-differential equations to auxiliary systems of ordinary differential equations. Re...

We analyse model problems of stress-induced atomic diffusion from a point source or from the surface of a material into an infinite or semi-infinite grain boundary, respectively. The problems are formulated in terms of partial differential equations which involve singular integral operators. The self-similarity of these equations leads to singular integro-differential equations which are solved...

This paper presents a numerical matrix method based on Bernstein polynomials (BPs) for approximate the solution of a system of m-th order nonlinear Volterra integro-differential equations under initial conditions. The approach is based on operational matrices of BPs. Using the collocation points,this approach reduces the systems of Volterra integro-differential equations associated with the giv...

the paper presents the semi-numerical solution for the magnetohydrodynamic (mhd) viscous flow due to a stretching sheet caused by boundary layer of an incompressible viscous flow. the governing partial differential equations of momentum equations are reduced into a nonlinear ordinary differential equation (node) by using a classical similarity transformation along with appropriate boundary cond...

The aim of this paper is solving nonlinear Volterra-Fredholm fractional integro-differential equations with mixed boundary conditions‎. ‎The basic idea is to convert fractional integro-differential equation to a type of second kind Fredholm integral equation‎. ‎Then the obtained Fredholm integral equation will be solved with Nystr"{o}m and Newton-Kantorovitch method‎.  ‎Numerical tests for demo...

In this paper, we study algorithmic aspects of linear ordinary integro-differential operators with polynomial coefficients. Even though this algebra is not noetherian and has zero divisors, Bavula recently proved that it is coherent, which allows one to develop an algebraic systems theory. For an algorithmic approach to linear systems theory of integro-differential equations with boundary condi...