In recent years, some promising approximate analytical solutions are proposed, such as exp-function method [1], homotopy perturbation method [2 – 11], and variational iteration method (VIM) [12 – 17]. The variational iteration method is the most effective and convenient one for both weakly and strongly nonlinear equations. This method has been shown to effectively, easily, and accurately solve ...

The Laplace decomposition method (LDM) has been implemented on integro-differential equations to calculate the analytical exact solutions. Obtained results show the effectiveness, reliability and convergence of the proposed method. It may be concluded that the proposed method is a powerful tool for solving the integro-differential equations and other wide class of mathematical problems.

This paper is concerned with existence of a C viscosity solution of a second order nontranslation invariant integro-PDE. We first obtain a weak Harnack inequality for such integroPDE. We then use the weak Harnack inequality to prove Hölder regularity and existence of solutions of the integro-PDEs.

Introducing shift operators on time scales we construct the integro-dynamic equation corresponding to the convolution type Volterra differential and difference equations in particular cases T = R and T = Z. Extending the scope of time scale variant of Gronwall’s inequality we determine function bounds for the solutions of the integro dynamic equation.

Fractional diffusions arise in the study of models from population dynamics. In this paper, we derive a class of integro-differential reactiondiffusion equations from simple principles. We then prove an approximation result for the first eigenvalue of linear integro-differential operators of the fractional diffusion type, and we study from that the dynamics of a population in a fragmented envir...

The nonFickian flow of fluid in porous media is complicated by the history effect which characterizes various mixing length growth of the flow, which can be modeled by an integro-differential equation. This paper proposes two mixed finite element methods which are employed to discretize the parabolic integro-differential equation model. An optimal order error estimate is established for one of ...

We apply a total variation minimization technique for the deblurring of two-dimensional images. This yields an integro-diierential equation with a nonlinear elliptic partial diierential operator. In this paper we discuss a numerical scheme for the eecient solution of this integro-diierential equation. Results are presented for a deconvolution problem arising in ground-based astronomical imaging.

A numerical scheme, based on the cubic B-spline wavelets for solving fractional integro-differential equations is presented. The fractional derivative of these wavelets are utilized to reduce the fractional integro-differential equation to system of algebraic equations. Numerical examples are provided to demonstrate the accuracy and efficiency and simplicity of the method.

In this paper, a numerical solution for a system of linear Fredholm integro-differential equations by means of the sinc method is considered. This approximation reduces the system of integro-differential equations to an explicit system of algebraic equations. The exponential convergence rate $O(e^{-k sqrt{N}})$ of the method is proved. The analytical results are illustrated with numerical examp...

We discuss the approximate controllability of nonlinear fractional integro-differential system under the assumptions that the corresponding linear system is approximately controllable. Using the fixed-point technique, fractional calculus and methods of controllability theory, a new set of sufficient conditions for approximate controllability of fractional integro-differential equations are form...