Consider the numerical integration of the differential equation

using the rectangular rule.

(a) Develop the difference equation, as in (6-25), for the numerical integration of this differential equation.

(b) Let r(t) = 1 , x(0) = 0 , and H = 0.1 . Use the z-transform to solve the difference equation of part (a) for x(1.0).

(c) Repeat part (b) for H = 0.01 .

(d) Solve the given differential equation, using the Laplace transform, for the exact value of x(1.0).

(e) Compare the errors in the results in parts (b) and (c).

Transcribed Image Text:

dx(t) + x(t) = r(t)