Available online at http://ijim.srbiau.ac.ir/ Int. J. Industrial Mathematics (ISSN 2008-5621) Vol. 8, No. 3, 2016 Article ID IJIM-00775, 7 pages Research Article Bernoulli operational matrix method for system of linear Volterra integral equations E. Hashemizadeh *† , M. Mohsenyzadeh ‡ Received Date: 2015-10-25 Revised Date: 2015-11-16 Accepted Date: 2016-02-11 ————————————————————————————————– Abstract In this paper, the numerical technique based on hybrid Bernoulli and Block-Pulse functions has been developed to approximate the solution of system of linear Volterra integral equations. System of Volterra integral equations arose in many physical problems such as elastodynamic, quasi-static visco-elasticity and magneto-electro-elastic dynamic problems. These functions are formed by the hybridization of Bernoulli polynomials and Block-Pulse functions which are orthonormal and have compact support on [0, 1]. By these orthonormal bases we drove new operational matrix which was a sparse matrix. By use of this new operational matrix we reduces the system of integral equations to a system of linear algebraic equations that can be solved easily by any usual numerical method. The numerical results obtained by the presented method have been compared with some existed methods and they have been in good agreement with the analytical solutions and other methods that prove the profit and efficiency of the proposed method. Keywords : System of Volterra integral equations; Bernoulli polynomials; Hybrid functions; Opera- tional matrix. —————————————————————————————————– 1 Introduction S ystem of linear Volterra integral equations arises in many physical applications, e.g., linear quasi-static visco-elasticity problem [2], magneto-electro-elastic dynamic problems [3] and the elastodynamic problems of piezoelectric [4]. We consider the following system of linear Volterra integral equations G(x)U (x)+ ∫ x 0 K(x, s)U (s)ds = F (x), i =1, 2, ..., q, (1.1) * Corresponding author. hashemizadeh@kiau.ac.ir † Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran. ‡ Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran. that U (x)=[u 1 (x), ..., u q (x)] T , F (x)=[f 1 (x), ..., f q (x)] T , (1.2) and G(x)=    g 11 (x) ··· g 1q (x) . . . . . . . . . g q1 (x) ··· g qq (x)    , K(x, s)=    k 11 (x, s) ··· g 1q (x) . . . . . . . . . g q1 (x) ··· g qq (x)    , where the functions g ij (t),f i (x) ∈ L 2 [0, 1) and the kernels k ij (x, s) ∈ L 2 ([0, 1) × [0, 1)) for i, j = 1, 2, ..., q are known and u i (x) for i =1, 2, ...q 201