Lab for the Adams Bashforth Moulton Method

Module for the Adams-Bashforth-Moulton Method

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Adams-Bashforth-Moulton Method for O.D.E's. To approximate the solution of the initial value problem with over by using the predictor

and the corrector
.

Report to be handed in.

Computer Problems.

Exercise 1. Solve the I.V.P. with y(0) = 0 over .
Use 40 subintervals of [0,10] to get your answer.
Plot the solution using 40 subintervals.
Report the last point which is the numerical approximation to (10, y(10)).

Exercise 2. Solve the I.V.P. with y(0) = 0 over [0.0, 10.0].
Use 100 subintervals of [0,10] to get your answer.
Plot the solution using 100 subintervals.
Report the last point which is the numerical approximation to (10, y(10)).

Remark. The value of y(10) is known to be:

Compare it with the last computed value.

For problems 3 - 5 we will use the I.V.P. .

Exercise 3. Solve .
Use 65 subintervals of [0,10] to get your answer.
Plot the solution using 65 subintervals.

Exercise 4. Solve
Use 37 subintervals of [0,10] to get your answer.
Plot the solution using 37 subintervals.

Exercise 5. Use Mathematica or techniques learned in calculus to obtain the analytic solution to the D.E.

Exercise 6. Graph the analytic solution to the D.E. found in problem 4.

Exercise 7. Read the textbook and see if you can find out something about difficulties with the step size when using a predictor-corrector method.

Exercise 8. Why does the solution in problem 4 exhibit a chaotic behavior ?

(c) John H. Mathews, 1998