Consider the numerical integration of the differential equation (6-24) in Section 6.6. Applying the rectangular rule results in the difference equation (6-25), which can be expressed as

(a) Use the z-transform to solve this equation as a function of x(0) and H.

(b) Use the results of part (a) to show that as given in Section 6.6, x(1.0) = 0.3487 with x(0) = 1 and H = 0.1 .

(c) Solve for x(1.0) with x(0) = 1 and H = 0.01 .

(d) The exact value of x(1.0) is given in Section 6.6. Compare the errors in the results of parts (b)
and (c).

Equation 6-24

Transcribed Image Text:

x[(k+1)H] = x(kH) + H[x(kH)]