Numerical solution of a special type of integro-differential equations

Numerical solving initial value problem for Fredholm type linear integro-differential equation system

“…where the double prime on the summation symbol here and elsewhere indicates that the terms with suffixes k ¼ 0 and N to be halved, and the points ft k g are (see [10][11][12]30,34,35]) Chebyshev collocation points We consider the differentiation of the function I n ðxÞ defined by the equation…”

“…In papers [30,31,[34][35][36] methods for the numerical solution of integral and IDEs have been proposed. The suggested methods are based on representing the solutions in the linear combination of Lagrange's fundamental polynomials and on approximating the integral term by the Clenshaw-Curtis quadrature formula.…”

Comparison of Adomian Decomposition and Taylor Expansion Methods for the Solutions of Fractional Integro-Differential Equations

“…The existence and uniqueness of solutions to fractional differential equations have been investigated [2,7,9,14]. In addition, when , Eq(1.1) reduces to linear integro-differential equation and the numerical methods for this equation have been extensively studied by many authors [8,12,15]. There are many methods for seeking approximate solutions such as collocation method, the fractional differential transform method, Legendre wavelet method, Taylor expansion method and Adomian decomposition method, See ([1, 4,5,10,13]).…”

Approximate solution of a class of linear integro-differential equations by Taylor expansion method

“…Hosseini and Shahmorad [7] proposed the Tau method to numerically solve Fredholm integro-differential equations with polynomial bases. Rashed [15] treated a special type of integro-differential equations with derivatives appearing in integrals.…”

“…Now we consider a Volterra integro-differential equation of the first kind[15] x 0 cos(x − t)y (t)dt = 2 sin x Downloaded by [University of Newcastle (Australia)] at 22:42 27 August 2014…”