A spectral collocation matrix method for solving linear Fredholm integro-differential–difference equations

Abstract

In this study, a spectral collocation matrix method has been introduced to solve the linear Fredholm integro differential–difference equation (LFIDDE) numerically. The method is combined Chebyshev series and matrix algebras. As it is assumed that the truncated second-kind Chebyshev series is a solution of the given LFIDDEs, the matrix form of the each part of LFIDDEs is put into the LFIDDEs which is transformed a matrix-vector equation. The coefficients of the truncated second-kind Chebyshev series are obtained to solving such a linear equation. The given method’s quality and reliability are shown in some numerical examples and comparisons of some methods