On improvement of the integral operational matrix in block pulse function analysis

Abstract

It has been shown by Chen and Chung (1987) that the use of the conventional kintegral operational matrix P in block pulse function (BPF) analysis is equivalent to evaluating the BPF coefficients of the integrated function by the well known trapezoidal rule. They have improved upon P by employing a three-point interpolation polynomial in the Lagrange form to develop a new integral operational matrix P1 (say). In the present paper, it has been established that once a function f(t) is represented by a BPF series, application of P to integrate f(t) in the staircase form is exact. Also, the method proposed by Chen and Chung (1987) is merely an extension of the trapezoidal rule wherein only one term of the remainder has been considered. Consideration of two terms from the remainder improves upon the integral operational matrix P1 further and this improved operational matrix P2 (say) has been employed to illustrate its superiority. Inclusion of still further terms from the remainder will improve upon P2 further, but the rate of improvement will diminish gradually as evident from the illustrative examples.