Abstract The main goal of this paper is to obtain error bounds for parabolic integro-differential equation. derivation these based elliptic and Ritz -Volterra reconstructions introduced by Makridakis Nochetto 2003 then extended - Volterra reconstruction in case integro-parabolic differential problems Reddy Sinha 2015. We proved optimal order certain classes semilinear intergro equations. key po...

In this article differential transformation method (DTMs) has been used to solve neutral functional-differential equations with proportional delays. The method can simply be applied to many linear and nonlinear problems and is capable of reducing the size of computational work while still providing the series solution with fast convergence rate. Exact solutions can also be obtained from the kno...

The Smoluchowski equation is a nonlinear integro-differential equation describing the evolution of the concentration μt(dx) of particles of mass in (x, x+ dx) in an infinite particle system where coalescence occurs. We introduce a class of algorithms, which allow, under some conditions, to simulate exactly a stochastic process (Xt)t≥0, whose time marginals are given by (xμt(dx))t≥0.

We establish some decay properties of the semigroup generated by a linear integro-differential equation in a Hilbert space, which is an abstract version of the equation ut(t)− β∆u(t)− ∫ ∞ 0 k(s)∆u(t− s)ds = 0 describing hereditary heat conduction.

Homotopy perturbation method is a well-known method for solving many functional equations such as differential equations, integral equations, integro-differential equations and so on. Applying this method needs some computations which are boring by hand. Therefore, creating a program to do all computations would be useful. In this work, a maple program is prepared to solve the second kind of Vo...

the spline collocation method  is employed to solve a system of linear and nonlinear fredholm and volterra integro-differential equations. the solutions are collocated by cubic b-spline and the integrand is approximated by the newton-cotes formula. we obtain the unique solution for linear and nonlinear system $(nn+3n)times(nn+3n)$ of integro-differential equations. this approximation reduces th...

A new class of numerical methods for Volterra integro-differential equations with memory is developed. The methods are based on the combination of general linear methods with compound quadrature rules. Sufficient conditions that guarantee global and asymptotic stability of the solution of the differential equation and its numerical approximation are established. Numerical examples illustrate th...