Solution of a functional differential equation via delayed unit step functions

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Abstract
A new set of delayed unit step functions (DUSFs) has been defined. Based on the approximations of the delay operators exp (−hs) and exp ( −αhs) o α  1) respectively by two new operational matrices of DUSFs ore derived. One is the integration matrix which relates DUSFs to their integrals, and the other is the stretch matrix which relates DUSFs to their stretched forms. By the use of these two operational matrices the solutions of a differential equation of the type [ydot] (t)= ay( are obtained in a series of DUSFs. The results obtained may be piecewise-constant or pointwise. Compared with Walsh or block pulse function approaches, the proposed method is simpler in the construction of its operational matrices, and is more amenable to computer programming.

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