Received 17 September 2011; revised 10 November 2011; accepted 17 November 2011. ———————————————————————————————Abstract In this paper, the fuzzy solution of non-linear fuzzy Volterra integro-differential equation (NFIDE) is approximated. To do this, we define a sequence of fuzzy functions which approximate the fuzzy solution of this type of equations and finally, we estimate upper bound of the...

This paper deals with the stability of Runge–Kutta methods for a class of stiff systems of nonlinear Volterra delay-integro-differential equations. Two classes of methods are considered: Runge–Kutta methods extended with a compound quadrature rule, and Runge– Kutta methods extended with a Pouzet type quadrature technique. Global and asymptotic stability criteria for both types of methods are de...

This paper presents meshfree method for solving systems of linear Volterra integro-differential equations with initial conditions. This approach is based on collocation method using Sinc basis functions. It's well-known that the Sinc approximate solution converges exponentially to the exact solution. Some numerical results are included to show the validity of this method.

In this paper, we apply the local fractional Laplace transform method (or Yang-Laplace transform) on Volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. The iteration procedure is based on local fractional derivative operators. This approach provides us with a convenient way to find a solution ...

A new and effective direct method to determine the numerical solution of specific nonlinear Volterra-Fredholm integral and integro-differential equations is proposed. The method is based on vector forms of block-pulse functions (BPFs). By using BPFs and its operational matrix of integration, an integral or integro-differential equation can be transformed to a nonlinear system of algebraic equat...

In this paper, we develop and modify Taylor-series expansion method to approximate a solution of nonlinear Volterra integro-differential equations (IDEs) as well as a solution of a system of nonlinear Volterra equations. By means of the nth-order Taylor-series expansion of an unknown function at an arbitrary point, a nonlinear Volterra equations can be converted approximately to a system of non...

The spatial discretization of initial-boundary-value problems for (nonlinear) parabolic or hyperbolic PDEs with memory terms leads to (large) systems of Volterra integro-differential equations (VIDEs). In this paper we study the efficient numerical solution of such systems by methods based on linear multistep formulas, using special factorization (or splitting) techniques in the iterative solut...

In this note, convex Homotopy perturbation method (HPM) is presented for the approximate solution of the linear Fredholm-Volterra integral and integro-differential equation. Convergence and rate of convergence of the HPM are proved for both equations. Five numerical examples are provided to verify the validity and accuracy of the proposed method. Example reveals that HPM is very accurate and si...

We study S-asymptotically ω-periodic mild solutions of the semilinear Volterra equation u′(t) = (a ∗ Au)(t) + f(t, u(t)), considered in a Banach space X, where A is the generator of an (exponentially) stable resolvent family. In particular, we extend recent results for semilinear fractional integro-differential equations considered in [4] and for semilinear Cauchy problems of first order given ...

In this manuscript, we analyze the solution for class of linear and nonlinear Caputo fractional Volterra Fredholm integro-differential equations with time varying delay. Also, demonstrate stability analysis these equations. Our paper provides a convergence semi-analytical approximate method It would be desirable to point out results.