Spreadsheet and Euler’s Method Exercises
The idea is to set up spreadsheets for several differential equations, with the options of working through the suggested homework problems, looking at some equations that come up in applications, or exploring modifications to Euler’s method which aim to produce greater accuracy. In each case, start by looking at the slope field defined by the equation (the URL is http://alamos.math.arizona.edu/ODEApplet/JOdeApplet.html)
A. The basic: y’ = y and y(0) = 1.0; find a solution for x between 0 and 5
B. The suggested homework problems from section 11.3 are 2, 6, 7, 9, 10. Not all are suitable for spreadsheets: keep your eyes open.
C. (a) the logistic equation: y’ = 0.5y - 0.005y2 ; y(0) = 0.1
(b) the spring equation: y’’ = - y; y(0) = 1.0 and y’(0) = 0.0. Note that this equation is second order, so you need to use Euler’s approach twice: once for the function y and once for its first derivative y’.
D. See handout from Rutgers: http://coewww.rutgers.edu/classes/bme/bme305/ODE/ODE_Lec1_20Nov03.htm