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 ...

In this paper, we present a mixed spline/spectral method to solve Volterra delay-integro-differential equations (VDIDEs). This method is based on generating the sextic spline collocation methods in all subintervals. The approximation of the integration in these subintervals, can be calculated by the El-Gendi method. Convergence results of the present method are presented. Numerical results are ...

We present an hp-error analysis of the discontinuous Galerkin time-stepping method for Volterra integro-differential equations with weakly singular kernels. We derive new error bounds that are explicit in the time-steps, the degrees of the approximating polynomials, and the regularity properties of the exact solution. It is then shown that start-up singularities can be resolved at exponential r...

In this paper, we analyze Levitan and Bebutov metrical approximations of functions $F :\Lambda \times X \rightarrow Y$ by trigonometric polynomials $\rho$-periodic type functions, where $\emptyset \neq \Lambda \subseteq {\mathbb R}^{n}$, $X$ $Y$ are complex Banach spaces, $\rho$ is a general binary relation on $Y$. We also various classes multidimensional almost periodic in metric uniformly rec...

*Correspondence: [email protected] Department of Mathematics, Faculty of Sciences, Yuzuncu Yil University, Van, 65080, Turkey Abstract We study the convergence properties of a difference scheme for singularly perturbed Volterra integro-differential equations on a graded mesh. We show that the scheme is first-order convergent in the discrete maximum norm, independently of the perturbation parame...

Integral and integro-differential equations are one of the most useful mathematical tools in both pure and applied mathematics. In this article, we present a variational iteration method for solving Fredholm integro-differential equations. This study provides an analytical approximation to determine the behavior of the solution. To show the efficiency of the present method for our proble...