Bernoulli operational matrix method for system of linear Volterra integral ‎equations

در اين مقاله، يك روش عددي براي تقريب جواب سيستم معادلات انتگرال ولترا خطي، بر اساس تركيب توابع برنولي و بلاك پالس گسترش داده شده. اين توابع از تركيب چند جمله اي هاي برنولي و توابع بلاك پالس ايجاد شده اند. اين توابع متعامد و روي بازه [0,1] داراي محمل فشرده هستند. روش پيشنهادي سيستم معادلات انتگرالي را به يك سيستم از معادلات جبري خطي تبديل مي كند كه مي تواند به هر روش عددي معمولي حل شود. نتايج عددي به دست آمده با روش پيشنهادي با تعدادي از نتايج روشهاي موجود و جوابهاي تحليلي مقايسه شده و نشان دهنده دقت قابل قبولي هستند و اين برتري و كارايي روش بيان شده را نشان مي دهد.

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.‎