In this paper we discuss the collocation method for a large class of Fredholm linear integro-differential equations. It will be shown that, when a certain higher order interpolation operation is added to the collocation solution of this equation, the new approximations will, under suitable assumptions, admit a multiterm error expansion in even powers of the step-size h. Based on this expansion,...

In this paper, a method based on the Tau method with arbitrary bases is developed to find the numerical solution of Fredholm integro-differential equations; the differential part appearing in the equation is replaced by its operational Tau representation. Some numerical results are given to demonstrate the superior performance of the Tau method, particularly, with the Chebyshev and Legendre bas...

We apply the polynomial least squares method to obtain approximate analytical solutions for a very general class of nonlinear Fredholm and Volterra integro-differential equations. The is relatively simple straightforward one, but its precision this type equations high, fact that illustrated by numerical examples presented. comparison with previous approximations computed included test problems ...

This paper concerns the implementation of orthogonal polynomials using Galerkin method for solving Volterra integro-differential and Fredholm equations. The constructed are used as basis functions in assumed solution employed. Numerical examples some selected problems provided results obtained show that with performed creditably well terms absolute errors obtained.

In the present article we study the stabilization of first-order linear integro-differential hyperbolic equations. For such equations we prove that the stabilization in finite time is equivalent to the exact controllability property. The proof relies on a Fredholm transformation that maps the original system into a finite-time stable target system. The controllability assumption is used to prov...

In this paper, an effective direct method to determine the numerical solution of linear and nonlinear Fredholm and Volterra integral and integro-differential equations is proposed. The method is based on expanding the required approximate solution as the elements of Chebyshev cardinal functions. The operational matrices for the integration and product of the Chebyshev cardinal functions are des...

This study aims to solve the most general form of linear mixed Volterra-Fredholm integro-differential equations multi-fractional order in Caputo sense (MV-FIFDEs), which is solved by using orthogonal generalized Bernstein’s polynomial expansion with collocation and moment discrete weighted residual method under suitable conditions; then, Clenshaw-Curtis formula applied approximate integral term...