In this paper will be compared between Adomian decomposition method (ADM) and Taylor expansion method (TEM) for solving (approximately) a class of fractional integro-differential equations. Numerical examples are presented to illustrate the efficiency and accuracy of the proposed methods. General Terms Numerical solutions, Fractional integro-differential equations.

The numerical stability of the polynomial spline collocation method for general Volterra integro-differential equation is being considered. The convergence and stability of the newmethod are given and the efficiency of the newmethod is illustrated by examples. We also proved the conjecture suggested by Danciu in 1997 on the stability of the polynomial spline collocation method for the higher-or...

In this paper, a modification of variational iteration method is applied to solve fractional integro-differential equations. The fractional derivative is considered in the Caputo sense. Through examples, we will see the modified method performs extremely effective in terms of efficiency and simplicity to solve fractional integro-differential equations. 2000 Mathematics Subject Classification: 6...

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.