Abstract. In this paper we use the contraction mapping theorem to obtain asymptotic stability results of the zero solution of a nonlinear neutral Volterra integro-differential equation with variable delays. Some conditions which allow the coefficient functions to change sign and do not ask the boundedness of delays are given. An asymptotic stability theorem with a necessary and sufficient condi...

The stability in L norm is considered for the Ritz Volterra projection and some applications are presented in this paper As a result point wise error estimates are established for the nite ele ment approximation for the parabolic integro di erential equation Sobolev equations and a di usion equation with non local boundary value problem This work is supported in part by NSERC CANADA Journal of ...

s of PhD Theses at Irish Universities 2007 On the Asymptotic Behaviour of Deterministic and Stochastic Volterra Integro–Differential Equations

The Sumudu decomposition method was used and developed in this paper to find approximate solutions for a general form of fractional integro-differential equation Volterra Fredholm types. Caputo definition deal with derivatives. As the under consideration depends mainly on writing non-linear terms, which are often found inside kernel integral equation, it Adomian’s polynomials well-known way. Af...

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...

In this paper, the new iterative method with a reliable algorithm is applied to the systems of Volterra integro-differential equations. The method is useful for both linear and nonlinear equations. By using this method, the solutions are obtained in series form. Two linear and one nonlinear system of the equations are given to verify the reliability and efficiency of the method. Beside this, th...

With reasonable control selections on the space of functions, various application models can take the shape of a well-defined control system on mathematics. In the credibility space, controlability management of fuzzy differential equation is as much important issue as stability. This paper addresses exact controllability for abstract fuzzy differential equations in the credibility space in the...

An efficient hybrid method is developed to approximate the solution of the high-order nonlinear Volterra-Fredholm integro-differential equations. The properties of hybrid functions consisting of block-pulse functions and Lagrange interpolating polynomials are first presented. These properties are then used to reduce the solution of the nonlinear Volterra-Fredholm integro-differential equations ...