Numerical solution of ordinary differential equations
MTH 452/552

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:

• Apply basic finite difference schemes for ODEs
• Identify the appropriate method for an ODE in a given application
• Assess stability and accuracy of schemes
• Describe and comprehend important concepts such as Consistency, Stability and Convergence

• Synthesize lower order formulas to generate higher order ones
• Analyze stability and accuracy properties of families of schemes
• Evaluate trade-offs of accuracy and efficiency of methods

Grade Distribution

Grade Scale