Example 10. Use Mathematica to find the analytic solution
and graph for the I.V.P.
Solution 10.
Solution 10.
Dig out the formula for the solution out of the data structure
of solset and put it in f[t].
Plot the analytic solution at the same sample points that
were used for the numerical approximations.
Just for fun, plot the Adams-Bashforth-Moulton solution and
the analytic solution. Notice that there is a difference.
Something strange is happening, it appears that the solution
has a vertical asymptote, yet Adams-BashforthMoulton's method is able to move past this asymptote! How
can this happen? If the step size is chosen smaller, then
these methods will not tend to overshoot the asymptote.
The location of the asymptote can be found using
Mathematica's procedure FindRoot.
Numerical methods with a higher order of precision will not
tend to overshoot the asymptote.
Various Scenarios and Animations for the AdamsBashforth-Moulton Method.
Example 11. Solve the I.V.P.
. Compute the Adams-Bashforth-Moulton solution to the
Solution 11.
Solution 11.
Animations (Adams-Bashforth-Moulton
Method Adams-Bashforth-Moulton Method). Internet
hyperlinks to animations.
Terima kasih
(c) John H. Mathews 2004
(c) John H. Mathews 2004