numerical solution of delay differential equations via operational matrices of hybrid of block-pulse functions and bernstein polynomials

in this paper, we introduce hybrid of block-pulse functions and bernstein polynomials and derive operational matrices of integration, dual, differentiation, product and delay of these hybrid functions by a general procedure that can be used for other polynomials or orthogonal functions. then, we utilize them to solvedelay differential equations and time-delay system. the method is based upon expanding various time-varying functions as their truncated hybrid functions. illustrative examples are included todemonstrate the validity, efficiency and applicability of the method.