Numerical solution of ordinary differential equations
MTH 452/552

MWF 10:00-10:50
Instruction via Canvas and Zoom
Winter 2021


Dr. Nathan Louis Gibson  



Office Hours:

MW noon-12:50

Course Website:

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

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:
  2. Search: 'Society of Industrial and Applied Mathematics'
  3. Click + Join Now. (Need OSU log-in)

Course Description

Catalog Description: Numerical solution of initial-value problems using Runge-Kutta methods and linear multistep methods; introduction to boundary-value problems. Analysis of stability, accuracy, and implementation of methods.
Credits: 3

In this 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.

Measurable Student Learning Outcomes: A successful student in MTH 452 will be able to:

A successful student in MTH 552 will additionally be able to:


The programming language for this course is MATLAB. Oregon State University has subscribed to a Total Academic Headcount (TAH) Site License for MATLAB. This new licensing includes many, but not all MATLAB toolboxes. OSU faculty, staff and students can install on up to 4 personally-owned devices or computers. For more information visit Information Services -- MATLAB.

The following are online resources for learning Matlab:


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 is required for this course. Assignments 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 will be posted on Canvas.

Assignments should be completed individually. You may confer with fellow students in general terms, but must write code and solutions on your own.


There will be one midterm exam and one cummulative final exam.


Last updated: Mon Feb 15 13:09:29 PST 2021