We derive formulae for the calculation of Taylor coefficients of solutions to systems of Volterra integral equations, both linear and nonlinear, either without singularities or with singularities of Abel type and logarithmic type. We also obtain solutions to certain systems of Volterra equations of the first kind. In all cases except the case of logarithmic singularities, we obtain recursive fo...

in this paper, we will present a review of the multistep collocation method for delay volterra integral equations (dvies) from [1] and then, we study the superconvergence analysis of the multistep collocation method for dvies. some numerical examples are given to confirm our theoretical results.

Volterra difference equations arise in the mathematical modeling of some real phenomena, and also in numerical schemes for solving differential and integral equations (cf. [7, 8] and the references therein). One of the basic methods in the theory of stability and boundedness of Volterra difference equations is the direct Lyapunov method (see [1, 3, 4] and the references therein). But finding th...

In this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear Volterra integral equations of the first and second kinds, which avoids from using starting values. An existence and uniqueness theorem is proved and convergence isverified by using an appropriate variety of the Gronwall inequality. Application of the method is demonstrated for solving the ...