In this article, we apply the operational matrix to find the numerical solution of two- dimensional nonlinear Volterra integro-differential equation (2DNVIDE). Form this prospect, two-dimensional shifted Legendre functions (2DSLFs) has been presented for integration, product as well as differentiation. This method converts 2DNVIDE to an algebraic system of equations, so the numerical solution o...

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 ...

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...