Math 435 Spring 2009 Prof. B. Datta
Additional Practice Exercises on Predictor-Corrector Metho d
1. Derive the predictor-corrector formula based on Euler’s method as the predictor and
trapezoidal rule of integration as the corrector.
2. Use the formula developed in 1 to solve the following equations with h= 0.5.
(a) y0=t2−y,y(0) = 1, 0 ≤t≤2
(Exact solution:y(t) = −e−t+t2−2t+ 2)
(b) y0=−t
y,y(1) = 1, 1 ≤t≤2
(Exact solution:y(t) = (2 −t2)1
2)
Compare the computed solution at each step with the exact solution.