Numerical solution of ordinary differential equations
MTH 452/552

MWF 10:00-10:50
Winter 2022

Professor:

Dr. Nathan Louis Gibson  

Office:

Kidder 056

Office Hours:

MWF 11-11:50

Course Website:  

https://sites.science.oregonstate.edu/~gibsonn/Teaching/MTH552-010W22/

Text Book
(for 452/552 and 453/553):  
Required






Randy LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM (SIAM Member price: $52.15)
So be sure to sign up for your free membership through our student chapter!


To formally become a member of the chapter, do the following
  1. Find an organization page: https://clubs.oregonstate.edu/findclubs
  2. Search: 'Society of Industrial and Applied Mathematics'
  3. Click + Join Now. (Need OSU log-in)


Course Description

In the course we will study algorithms for the numerical solution of initial-value problems using Runge-Kutta methods and linear multistep methods, as well as provide an introduction to boundary-value problems. Analytical (stability, accuracy, and convergence) and practical (implementation) properties of these methods will be examined. Students will get computational experience in applying the algorithms studied using the MATLAB problem-solving environment.

Specifically, we will begin by analyzing systems of linear ODEs, discuss one-step and multi-step methods including predictor-corrector methods. Then we will discuss zero-stability, absolute stability and stability regions for various methods. Lastly, we will describe the problem of stiff ODEs and examine methods which may help.

Prerequisites: Familiarity with basic properties of differential equations (MTH 256) and matrices (MTH 341 or 306), and some programming experience (preferably with MATLAB) is required. Those who have taken the equivalent of MTH351 or MTH451/551 would be well-prepared. Students who are not sure about prerequisites are encouraged to talk to me.


Matlab

The programming language for this course is MATLAB. You can obtain access to MATLAB via one of the following:


Grades

Grade Distribution

Homework 40%
Midterm 30%
Final 30%
Total 100%

Grade Scale

A 93
A- 90
B+ 87
B 83
B- 80
C+ 77
C 73
C- 70
D+ 67
D 63
D- 60


Homework

Homework assignments will be posted here as pdf files. They will be mostly self-contained, but possibly referencing problems from the text book. Some problems will require programming and/or computational experimentation. This is not a programming course, thus many algorithms will be coded for you. However, you will need to know how to fix, modify and use MATLAB codes.

Assignments should be completed individually. You may confer with fellow students in general terms, but must write code and solutions on your own. 552: denotes a problem that is required only for students enrolled in MTH 552, but can serve as extra credit for MTH 452 students.
452: denotes a problem that is optional for MTH 552 students.


Exams

There will be one midterm exam on Friday Feb 12, and one cummulative final exam Tuesday Mar 16 at 6PM.


Links


Last updated: Mon Jan 03 12:38:29 PST 2022