Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where . Stability and convergence in  norm are discussed through energy method. Numerical examples are provided to confirm the theoretical prediction ...

In this work we consider a partial integro-differential equation. We reformulate it a functional integro-differential equation in a suitable Hilbert space. We apply the method of lines to establish the existence and uniqueness of a strong solution.

in this paper, first the properties of one and two-dimensional differential transforms are presented.next, by using the idea of differential transform, we will present a method to find an approximate solution fora volterra integro-partial differential equations. this method can be easily applied to many linear andnonlinear problems and is capable of reducing computational works. in some particu...

Abstract: The aim of study is to solve parabolic integro-differential equation with a weakly singular kernel. Problems involving partial integro-differential equations arise in fluid dynamics, viscoelasticity, engineering, mathematical biology, financial mathematics and other areas. Many mathematical formulations of physical phenomena contain integro-differential equations. Integro-differential...

In this paper we study the existence of classical solutions for a class of abstract neutral integro-differential equation with unbounded delay. A concrete application to partial neutral integro-differential equations is considered.

In this article two algorithms, one based on variation iteration method and the other on Adomian's decomposition method, are developed to find the numerical solution of an initial value problem involving the nonlinear integro-differential equation , , , where R is a nonlinear operator that contains partial derivatives with respect to x. Special cases of the integro-differential equation are sol...

In this work first we consider a physiologically structured population model with a distributed recruitment process. That is, our model allows newly recruited individuals to enter the population at all possible individual states, in principle. The model can be naturally formulated as a first order partial integro-differential equation, and it has been studied extensively. In particular, it is w...

We consider the following partial integro-differential equation (Allen–Cahn equation with memory): φt = ∫ t 0 a(t − t ′)[ ∆φ + f (φ)+ h](t ′) dt ′, where is a small parameter, h a constant, f (φ) the negative derivative of a double well potential and the kernel a is a piecewise continuous, differentiable at the origin, scalar-valued function on (0,∞). The prototype kernels are exponentially dec...

A linear partial integro-differential equation is solved both numerically and analytically using variational iteration method. This equation typically arises in viscoelasticity and other areas. The analytic solution is represented by an infinite series.