A new collocation method for solution of mixed linear integro-differential-difference equations

Abstract

The aim of this article is to present an efficient numerical procedure for solving mixed linear integro-differential-difference equations. Our method depends mainly on a Taylor expansion approach. This method transforms mixed linear integro-differentialdifference equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equation. The reliability and effiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer program in Maple10.

An improved Morgan-voyce collocation method for numerical solution of multi-pantograph equations

“…(1), we replace the row matrice (13) by the last one row of the matrix (12), so have the new augmented matrix [15,16,17]…”

Modelling of Displacement Washing of Pulp Fibers Using the Hermite Collocation Method

“…To overcome this problem, the Hermite collocation method (HCM) was proposed, which is the combination of Hermite interpolating polynomials and the orthogonal collocation technique. In the Hermite collocation method cubic Hermite interpolating polynomials are used as base functions to approximate the trial function (Dyksen & Lynch, 2000;Lang & Sloan, 2002;Jung, 2003;Liu et al, 2005;Ma et al, 2006;Finden, 2007;Mazroui et al, 2007;Han, 2009;Ricciardi & Brill, 2009;Gülsu et al, 2011;Yalçinbaş et al, 2011;Orsini et al, 2011). To apply the collocation technique, the residual is set equal to zero at the collocation points.…”

A Chebyshev-Gauss-Radau Scheme For Nonlinear Hyperbolic System Of First Order

“…Meanwhile, numerical treatments based on Chebyshev collocation method for some partial differential equations are introduced in [54,55,56]. Moreover, Chebyshev collocation methods were introduced for numerically solving integral equations [57,58] and integro-differential equations [59,60].…”