The work handles a Fredholm integro-differential equation involving boundary layers. A fitted second-order difference scheme has been created on uniform mesh utilizing interpolating quadrature rules and exponential basis functions. stability convergence of the proposed discretization technique are analyzed one example is solved to display advantages presented technique.

In this article we use discrete collocation method for solving Fredholm–Volterra integro– differential equations, because these kinds of integral equations are used in applied sciences and engineering such as models of epidemic diffusion, population dynamics, reaction–diffusion in small cells. Also the above integral equations with convolution kernel will be solved by discrete collocation metho...

n this paper, we study the existence and uniqueness of an intuitionistic fuzzy solution for semi-linear integro-differential equations with non-local conditions using Banach fixed point theorem. Theorem on these problems nonlocal are presented under certain assumptions. Finally, example is established to illustrate effectiveness

This paper concerns the implementation of orthogonal polynomials using Galerkin method for solving Volterra integro-differential and Fredholm equations. The constructed are used as basis functions in assumed solution employed. Numerical examples some selected problems provided results obtained show that with performed creditably well terms absolute errors obtained.

Abstract In this study, linear Fredholm fractional integro-differential equations (FIDEs) are numerically solved, where the derivative is considered in Caputo sense. work, least squares method (LSM) using a compact combination of shifted Chebyshev polynomials (SCP) first Kind applied to solving class FIDEs. Our aim write unknown function as series SCP, and then reduce problem system algebraic e...

A new and effective direct method to determine the numerical solution of specific nonlinear Volterra-Fredholm integral and integro-differential equations is proposed. The method is based on vector forms of block-pulse functions (BPFs). By using BPFs and its operational matrix of integration, an integral or integro-differential equation can be transformed to a nonlinear system of algebraic equat...

In this study, Chebyshev polynomials have been applied to construct an approximation method attain the solutions of linear fractional Fredholm integro-differential equations (IDEs). By method, IDE has transformed into a algebraic system with aid collocation points. conformable derivatives calculated in terms polynomials. Using results these calculations, matrix relation for was attained first t...

In this paper, fuzzy variational iteration method (FVIM) is proposed to solve the second- order fuzzy Abel-Volterra integro-differential equations. The existence and uniqueness of the solution and convergence of the proposed method are proved in details. is investigated to verify convergence results and to illustrate the efficiently of the method.

The Sumudu decomposition method was used and developed in this paper to find approximate solutions for a general form of fractional integro-differential equation Volterra Fredholm types. Caputo definition deal with derivatives. As the under consideration depends mainly on writing non-linear terms, which are often found inside kernel integral equation, it Adomian’s polynomials well-known way. Af...

In this paper, a new approach for solving the second order fuzzy differential equations (FDE) with fuzzy initial value, under strongly generalized H-differentiability is presented. Solving first order fuzzy differential equations by extending 1-cut solution of the original problem and solving fuzzy integro-differential equations has been investigated by some authors (see for example cite{darabi...