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

✍ Scribed by Anish Deb; G. Sarkar; Sunit K. Sen; Manabrata Bhattacharjee

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 447 KB
• Volume: 332
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(95)00057-7

✦ Synopsis

t has been shown by Chen and Chuny (1987) that the use of the conventional rcintegral operational matrix P in block pulse funetion (BPF) analysis is equivalent to evaluatin9 the BPF coefficients of the inteyrated function by the well known trapezoidal rule. They have improved upon P by employiny a three-point interpolation polynomial in the Layrange form to develop a new inteyral 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 inteyrate f(t) in the staircase form is exact. Also, the method proposed by Chen and Chun 9 (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 inteyral operational matrix PI 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 yradually as evident from the illustrative examples.