ExerciseODEsadvanced

Exercise: explicit versus predictor-corrector

Comparing the maximum error of AB2, AB4 and the predictor-correctors ABM2 and ABM4 on the same Verhulst IVP.

Error comparison

On the Verhulst IVP y′(t)=(3−0.1 y) yy'(t)=(3-0.1\,y)\,y, y(0)=10y(0)=10, the maximum errors are compared against the analytic solution y(t)=301+2e−3ty(t)=\frac{30}{1+2e^{-3t}}.

MethodMaximum error
AB2 (explícito)0.0613
ABM2 (predictor-corrector)0.0157
AB4 (explícito)0.0029
ABM4 (predictor-corrector)2.5127·10⁻⁴