numerical approximation based on bernouli polynomials for solving second-order hyperbolic telegraph equations

In this paper, a practical matrix method is presented for solving a particular type of telegraphequations. this procedure is based on bernouli polynomials. this matrix method with collocationsuited nodes, decreases the supposed equations into system of algebric equations with unknownbernouli coefficients. the obtained system is solved and approximate solutions are achieved. thewell-conditioning of problems is also considered. the indicated method creates the well-conditionedproblems. some numerical problems are comprised to confirm the efficacy and fitting of the suggested method. the presented technique is easy to implement and produces accurate results. theprecision of the method is demonstrated by measuring the errors between exact solutions and approximate solutions for each problem.