Department of Mathematics and Computer Science

Machine Problem 6

CS/Math 166 -- Winter, 2018 D. C. Smolarski, S.J.

20 points DUE: noon: Monday, March 12, 2018

Section 5.9 of Burden, Faires and Burden (10th ed, pp 331-340; 9th ed, pp 328-339; 8th ed, pp 313-325) describes the procedure used to solve a higher-order differential equation using the 4th order Runge-Kutta method. What one does is transform the higher-order ODE into a coupled system of first-order ODEs and use a vector of variables instead of a simple variable in the major steps. An example is also given (Example 1, p. 336 in the 10th ed.).

Write and execute a program to solve the second-order ODE (IVP):

Try to use Matlab/Octave to write this program (since it provides an easy-to-correct and debug environment and is a good exercise). If necessary, you can also use another language (e.g., C++).

Let the initial condition be x = 0, y = 1, y' = 2. Find the function over the interval [0,2] via h = delta-x increments of .05 (i.e., give output of 41 values of (x,y)).

As usual, your completed program may be turned in to my office, O'Connor 7, or to my mailbox in O'Connor 31. Please staple the pages yourself and do not turn in disconnected pages!

This page is maintained by Dennis C. Smolarski, S.J. Email: dsmolarski "at" scu.edu
Last changed: 21 October 2017