COMPUTER SCIENCE 614
Numerical Solution of Ordinary Differential Equations
SPRING 2012
COURSE INFORMATION
January 9
Prerequisites: The course will be self-contained as much as possible. Material needed from the
official prerequisite, CS 514, will be reviewed minimally. Assumed are (undergraduate) courses on
differential equations and linear algebra and a graduate course in continuous mathematics, e.g., CS
514, Math 527, or ME 581.
Instructor:
Robert Skeel
1205 LWSN
49-49025
skeel at cs.purdue.edu
Office hours:
Mondays 1:30–2:00
and by appointment
Examination dates:
Friday, March 2, in class,
Friday, April 20, in class.
Textbook:
An excellent book for much of the material is
NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS: INITIAL VALUE
PROBLEMS
David F. Griffiths and Desmond J. Higham, Springer, 2010.
This is supplemented by notes. Other references:
• Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations,
U. M. Ascher and L. R. Petzold, SIAM, Philadelphia, 1998.
• A First Course in the Numerical Analysis of Differential Equations,
Arieh Iserles, Cambridge University Press, 1996.
These other books will be on reserve in the Mathematical Sciences Library.
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Topics
with approximate dates:
Jan 9–18 initial value problems,
Jan 20–27 basic methods and concepts,
Jan 30 Taylor method,
Jan 30–Feb 8 multistep methods,
Feb 10-22 differential-algebraic equations,
Feb 22–Mar 19 stochastic differential equations,
Mar 21–30 one-step methods,
Apr 2–6 geometric integrators,
Apr 6–9 delay-differential equations,
Apr 11 coarse-graining,
Apr 11–27 boundary value problems.
Policies
a. Evident collaboration is penalized in accordance with university rules and the instructor’s
policy is to impose substantial penalties. This does not, of course, preclude some discussion
when starting an assignment. However, the onus is on you to ensure that the collaboration is
sufficiently limited that it is not evident in your work. Use of your work by another will be
assumed to be done with your consent unless there is evidence to the contrary.
b. Excuses. Failure to attend an exam or failure to submit an assignment on time is recorded as
a zero except when it is unavoidable because of some legitimate emergency (a medical excuse
from a physician, or a death in the immediate family). In such a case it is desirable that the
instructor be contacted before the exam or before the due date of the assignment.
Assignments
a. There will be about four homework sets and two other assignments requiring the use of the
computer or mathematical proofs. Tentative due dates are Jan 27, Feb 10, Mar 24, Mar 9,
Mar 30, and Apr 13.
b. Each student will present two 25-minute lectures on specified material Jan 30–Feb 8 and Mar
21–30.
c. Attendance during the the last three weeks (of April) is rewarded with points.
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Grading
assignments
hourlies
lectures
attendance
46%
32%
18%
4%
A
B
C
85-100%
70-85%
55-70%
D
F
45-55%
0-45%
The grade boundaries may be lowered by as much as 10% in order to achieve a reasonable grade
distribution. Also, there may be minor upward or downward adjustments of the grade boundaries.
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