Consider the numerical integration of the differential equation

using the predictor-corrector of Section 6.6. The predictor method is the rectangular rule, and the corrector method is the trapezoidal rule.

(a) Develop the difference equation, for the numerical integration of the given differential equation. The result should be one difference equation for x(kH) as a function of and the input function  .

(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 = 0.33333 .

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

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

Transcribed Image Text:

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