In this paper, by using the theories and methods of integral equation and computer algebra, a reliable algorithm for solving the Volterra integral equation is established, and a new Maple algorithm mainproc is established, too. Some examples are presented to illustrate the implementations of the algorithm. The results of the examples indicate that the algorithm of Taylor polynomial method is si...

Abstract This paper presents an appropriate numerical method to solve nonlinear Fredholm integro-differential equations with time delay. Its approach is based on the Taylor expansion. This method converts the integro-differential equation and the given conditions into the matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Taylor expansion coefficients, s...

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...

Adomian decomposition method has been applied to solve many functional equations so far. In this article, we have used this method to solve the fuzzy differential equation under generalized differentiability. We interpret a fuzzy differential equation by using the strongly generalized differentiability. Also one concrete application for ordinary fuzzy differential equation with fuzzy input data...

In this paper, we propose a method to approximate the solution of a linear Fredholm integro-differential equation by using the Chebyshev wavelet of the first kind as basis. For this purpose, we introduce the first Chebyshev operational matrix of integration. Chebyshev wavelet approximating method is then utilized to reduce the integro-differential equation to a system of algebraic equations. Il...

In this article we have considered Fredholm integro-differential equation type second-order boundary value problems and proposed a rational difference method for numerical solution of the problems. The composite trapezoidal quadrature and non-standard difference method are used to convert Fredholm integro-differential equation into a system of equations. The numerical results in experiment on s...

The homotopy analysis method [1, 2], is developed to search the accurate asymptotic solutions of nonlinear problems. This technique has been successfully applied to many nonlinear problems such as the viscous flows of non-Newtonian fluids [3, 4], the Korteweg-de Vries-type equations [5, 6], nonlinear heat transfer [7, 8], finance problems [9, 10], Riemann problems related to nonlinear shallow w...

in this paper, we interpret a fuzzy differential equation by using the strongly generalized differentiability concept. utilizing the generalized characterization theorem. then a novel hybrid method based on learning algorithm of fuzzy neural network for the solution of differential equation with fuzzy initial value is presented. here neural network is considered as a part of large eld called n...

Coarsening of solutions of the integro-differential equation

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...