Predictor Corrector Method; Adam Bashforth Moulton Method

Let's consider again the initial value problem
dy/dt = t*exp(3*t) - 2*y
y(0) = 0
0 <= t <= 2
A Matlab script to solve this problem that employs the Adam Bashforth Moulton predictor-corrector method can be downloaded here . It uses the functions deriv.m and exact.m .

Results (in comparison to an RK4 scheme) are

adam_b_m.jpg

Let's take a look at some numbers .
RK4 performs slightly better.
But: For many problems, implicit schemes allow us to take larger timestep.