
EXERCISES
3.4 In Examples 3.2 and 3.3,
(a) Explain why the implicit Euler integrator produces higher estimates of the continuous-time
integrator output than the explicit Euler integrator. Is this true in general?
(b) Find x
A
(5) for both numerical integrators and compare the results to x(0.25). Explain why
both integrators incur the maximum error jx(nT) x
A
(n)j for n ¼5.
(c) Repeat Examples 3.2 and 3.3 with a step size T ¼0.01. Enter the numerical results in a
table rounded to six places after the decimal point.
3.5 The RC circuit shown in Figure E3.5 is a first-order low-pass filter. The differential equation
relating the output voltage v
0
(t) and input ...