Mathematics 507: Numerical ODE

Instructor:

Roger Alexander
444 Carver Hall
(29)4-7579
alex at iastate dot edu

Consulting Hours:

Monday, Tuesday 12:30--2:30,
Thursday 3:00--4:00

Texts:

U. Ascher, R. Mattheij & R. Russell, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, Society for Industrial and Applied Mathematics, 1995.
R. Alexander, A Primer of Numerical Ordinary Differential Equations, on Project Vincent in the directory /home/mathclasses/alex/507/Notes
This page is http://www.math.iastate.edu/alex/507/syllabus.html
Consult the Math 507 schedule webpage for reading and homework assignments.

Topics:

INITIAL-VALUE PROBLEMS (7 weeks) Algorithms: Runge-Kutta, extrapolation and multistep methods. Stable methods for stiff problems. Analysis: Conditioning of initial value problems. Consistency, stability, and convergence of numerical methods; asymptotic behavior of error. Singular perturbations and stiff problems. Software: Implementation strategies; software libraries.
BOUNDARY-VALUE PROBLEMS (8 weeks) Algorithms: Shooting and multiple shooting; difference schemes, collocation. Analysis: Conditioning of boundary value problems. Consistency, stability and convergence. Software: Implementation strategies, software libraries.

Required work:

[60%] Problem Sets (about 6) containing both analytical and computational problems.
[25%] Computer Laboratory Projects (about 2) entailing either software implementation or the solution of a significant computational problem.
[15%] Final Exam