urysohn integral equation is one of the most applicable topics in both pure and applied mathematics. the main objective of this paper is to solve the urysohn type fredholm integral equation. to do this, we approximate the solution of the problem by substituting a suitable truncated series of the well known legendre polynomials instead of the known function. after discretization of the problem o...

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 computational method for numerical solution of a nonlinear volterra and fredholm integro-differentialequations of fractional order based on chebyshev cardinal functions is introduced. the chebyshev cardinaloperational matrix of fractional derivative is derived and used to transform the main equation to a system ofalgebraic equations. some examples are included to demonstrate the validity and ...

Abstract. This paper is concerned with a model system for radiation hydrodynamics in multiple space dimensions. The system depends singularly on the light speed c and consists of a scalar nonlinear balance law coupled via an integral-type source term to a family of radiation transport equations. We first show existence of entropy solutions to Cauchy problems of the model system in the framework...

In this paper, the Adomian decomposition method and Modified Technique are successfully applied to find approximate solutions of fuzzy system Volterra integro-differential equations. The obtained have been improved by using iteration integral equation numerical solution with Simpson rule Trapezoidal rule. These proposed methods gave excellent results close exact solution. show that present is v...

In this article, we consider the analogue of the Dirichlet problem for second-order elliptic integro-differential equations, which consists in imposing the “boundary conditions” in the whole complementary of the domain. We are looking for conditions on the differential and integral parts of the equation in order to ensure that the Dirichlet boundary condition is satisfied in the classical sense...

We study a scalar integro-differential conservation law. The equation was first derived in [2] as the slow erosion limit of granular flow. Considering a set of more general erosion functions, we study the initial boundary value problem for which one can not adapt the standard theory of conservation laws. We construct approximate solutions with a fractional step method, by recomputing the integr...

A linear completely nonhomogeneous generally nonlocal multipoint problem is investigated for a fourth-order differential equation with generally nonsmooth coefficients satisfying some general conditions such as pintegrability and boundedness. A system of five integro-algebraic equations called an adjoint system is introduced for this problem. A concept of a Green functional is introduced as a s...

In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...