Convergence analysis of Bernoulli matrix approach for one-dimensional matrix hyperbolic equations of the first order

In this paper, an approximate approach based on Bernoulli operational matrices has been presented to obtain the numerical solution of first-order matrix hyperbolic partial differential equations under the given initial conditions. After using the operational matrices, we use the completeness of Bernoulli basis in which the main problem reduces to a system of algebraic equations. The solutions of this algebraic system are the coefficients of the truncated double Bernoulli series which are defined in the interval [0, 1]. Also, convergence analysis associated to the presented idea is provided under several mild conditions. Several numerical examples are considered to show the efficiency of the technique.