We analyze the optimal superconvergence properties of piecewise polynomial collocation solutions on uniform meshes for Volterra integral and integrodifferential equations with multiple (vanishing) proportional delays θj(t) = qjt (0 < q1 < · · · < qr < 1). It is shown that for delay integro-differential equations the recently obtained optimal order is also attainable. For integral equations with...

In this article we use discrete collocation method for solving Fredholm–Volterra integro– differential equations, because these kinds of integral equations are used in applied sciences and engineering such as models of epidemic diffusion, population dynamics, reaction–diffusion in small cells. Also the above integral equations with convolution kernel will be solved by discrete collocation metho...

We consider finite element methods applied to a class of quasi parabolic integro-differential equations in R. Global strong superconvergence, which only requires that partitions are quasi-uniform, is investigated for the error between the approximate solution and the Sobolev-Volterra projection of the exact solution. Two order superconvergence results are demonstrated in W (Ω) and Lp(Ω), for 2 ...

The theory of a class of spectral methods is extended to Volterra integrodifferential equations which contain a weakly singular kernel (t − s)−μ with 0 < μ < 1. In this work, we consider the case when the underlying solutions of weakly singular Volterra integro-differential equations are sufficiently smooth. We provide a rigorous error analysis for the spectral methods, which shows that both th...

The time-dependent Maxwell system is supplemented with the constitutive relations of linear bianisotropic media and is treated as a neutral integro-differential equation in a Hilbert space. By using the theory of abstract Volterra equations and strongly continuous semigroups we obtain general well-posedness results for the corresponding mathematical problem.

In this article, block BS methods are considered for the numerical solution of Volterra integro-differential equations (VIDEs). Convergence and stability properties are analyzed. A new Matlab code for the solution of VIDEs, called VIDEBS, is presented. Numerical results using a variable stepsize implementation show the effectiveness of the proposed code. 2014 Elsevier Inc. All rights reserved.

In this paper, we formulate and analyze a new model for solving optimal control problems governed by Volterra integro-differential equations. The control and state variables are approximated by using monic Chebyshev series. The optimal control problem is reduced to a constrained optimization problem. Numerical examples are solved to show good ability and accuracy of the present approach.

The fuzzy set theory introduced by Zadeh has emerged as an interesting and fascinating branch of pure and applied sciences. The applications of fuzzy set theory can be found in many branches of regional, physical, mathematical, differential equations andengineering sciences. Recently, the authors have made important research results in the theory of fuzzy differentialequations, integrodifferent...

We analyse the asymptotic behaviour of integro-differential equations modelling N populations in interaction, where interactions are modelled by non-local terms involving linear combinations of the total number of individuals in each population. These models have already been shown to be suitable for the modelling of drug resistance in cancer. They also generalise the usual Lotka-Volterra ordin...

We investigate an h-p version of the continuous Petrov-Galerkin method for the nonlinear Volterra functional integro-differential equations with vanishing delays. We derive h-p version a priori error estimates in the L-, Hand L-norms, which are completely explicit in the local discretization and regularity parameters. Numerical computations supporting the theoretical results are also presented.