A pseudospectral method for the solution of second-order integro-differential equations

Abstract

In this paper we present a computational technique for solving the second-order Fredholm integro-differential equations. The method is based on a non-classical pseudospectral method. The differential matrices are computed and are utilized to reduce the second-order Fredholm integro-differential equations to algebraic equations. Numerical examples are presented to demonstrate the validity and applicability of the new method.

On Solutions of Linear Functional Integral and Integro-Differential Equations via Lagrange Polynomials

“…In recent years, various techniques have been used for solving FIDEs such as He's variational iteration technique [11], the homotopy perturbation method [12], He's homotopy perturbation method [13], the modified homotopy perturbation method [14], the rationalized Haar functions method [15], the Chebyshev cardinal functions method [16], the differential transformation method [17], the Tau method with error estimation [18], He's variational iteration method [19], the collocation method [20], the Adomian decomposition method [21], the Adomian-Pade technique [22], the discontinuous Galerkin method [23], the Legendre multiwavelets [24], the trigonometric wavelets [25], the spectral methods [26,27] the meshless method [28] and etc [35,40,41,[43][44][45][46][47][48][49][50]52]. In addition, the operation matrix method, the Galerkin-like method and the matrix-collocation methods based on Taylor, Chebyshev, Bessel, Bernoulli, Laguerre, Bernstein, Legendre, Chebyshev, Morgan-Voyce, Taylor-Lucas, Dickson and Lucas, polynomials, have been studied by some authors [29][30][31][32][33][34]42,51] to solve the mentioned type equations.…”