MCS 471 Computer Problem 4: Numerical Solution of ODEs
using Maple
Due: Friday 02 May 1997
Background Reading: Gerald and Wheatley, Chapter 5 & 6
Topics
5.3 Euler Methods
5.4 Runge-Kutta Methods
5.5 Multistep Methods
5.7 Adams-Moulton Multistep (PECE) Method
5.9-5.10 Convergence and Errors
6.1-6.2 Shooting Method and Solution of Sets of Equations
Maple Computer Problem:
Comparison of Several Numerical ODE System Methods
You must hand in a Maple worksheet that is well documented with
comments and plots of solutions.
Refer to the Class Maple Pages, or in particular to the
See also the Maple Language Help for DEtools, DEplot and their options.
The Model:
Find the solution of the following two-dimensional ODE (seasonal
predator-prey) system:
- x'(t) = (b(t) - a*y)*x
- y'(t) = (c + a*x)*y
where
- a:=0.471;
- c:=-0.0123;
- b(t)=3*(1 + 0.5*sin(3*t));
with initial conditions (IC):
Remark 1: Since ODE methods work as well for systems of vector ODEs,
you should compare the results for the following methods with
starting value t = 0.00 and stepsize h = 0.04 until
t = 8.00.
Use the following two methods of the Maple DEtools package with DEplot:
The Methods:
- YEM:. Euler's method (EM; called 'method=euler' option in DEplot).
- YRK4:. Runge-Kutta 4th order method (RK4, default method in DEplot).
Note that you will need to hand in plots along with Maple worksheets
and explain the difference in the approximations for this assignment.
Web Source: http://www.math.uic.edu/~hanson/M471/mcs471cp4.html
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