A linear approximation for solutions of Abel–Volterra integral equations

Acceptable Solutions of Linear Interval Integral Equations

I. Acceptable Solutions Let us consider an integral equation of the form 1 I k(s,t)x(t) dt = y(s) (1) o where x E X, Y E Y, k E K. We assume that X and Yare linear spaces of real functions on [0,1] and K ;s a suitable collection of real functions on [0,1]2. v, v (s) : = I k(s , t) u(t) dt o we can rewrite the equation (1) in the form Ax = y • (2) Suppose we have calculated an x E Xwith Ax ~ y, ...

A fractional type of the Chebyshev polynomials for approximation of solution of linear fractional differential equations

In this paper we introduce a type of fractional-order polynomials based on the classical Chebyshev polynomials of the second kind (FCSs). Also we construct the operational matrix of fractional derivative of order $ gamma $ in the Caputo for FCSs and show that this matrix with the Tau method are utilized to reduce the solution of some fractional-order differential equations.

Approximate Analytical Solutions of Fuzzy Linear Fredholm Integral Equations by HAM

A Numerical Approach for Solving of Two-Dimensional Linear Fredholm Integral Equations with Boubaker Polynomial Bases

In this paper, a new collocation method, which is based on Boubaker polynomials, is introduced for the approximate solutions of a class of two-dimensional linear Fredholm integral equationsof the second kind. The properties of two-dimensional Boubaker functions are presented. The fundamental matrices of integration with the collocation points are utilized to reduce the solution of the integral ...

Numerical approximation for integral equations

A numerical algorithm, based on a decomposition technique, is presented for solving a class of nonlinear integral equations. The scheme is shown to be highly accurate, and only few terms are required to obtain accurate computable solutions. 1. Introduction. Adomian polynomial algorithm has been extensively used to solve linear and nonlinear problems arising in many interesting applications (see...