TY - JOUR T1 - Numerical approximation based on the Bernouli polynomials for solving Volterra integro-differential equations of high order TT - تقریب عددی بر پایه چند جمله ایی های برنولی برای حل معادلات دیفرانسیل انتگرال ولترا از مراتب بالاتر JF - khu-mmr JO - khu-mmr VL - 3 IS - 2 UR - http://mmr.khu.ac.ir/article-1-2594-en.html Y1 - 2017 SP - 19 EP - 32 KW - ‎ ‎I‎ntegro-differential equations KW - ‎Bernouli‎ polynomials KW - Operational matrix‎. N2 - In this ‎article‎‎, ‎an ‎ap‎plied matrix method, which is based on Bernouli Polynomials, has been presented to find approximate solutions of ‎high order ‎Volterra ‎integro-differential‎ equations. Through utilizing this approach, the proposed equations reduce to a system of algebric equations with unknown Bernouli coefficients. A number of numerical ‎illustrations‎ have been ‎solved‎ to ‎assert‎ the ‎credibility‎ and ‎practically‎ of ‎this‎ ‎method M3 10.29252/mmr.2.3.19 ER -