Numerical solution of partial differential equations
MTH 453/553

This course will explore numerical methods based on finite difference discretizations for solving partial differential equations (PDEs), including time dependent. Partial differential equations are used to describe a large variety of physical phenomenon, from fluid flow to electromagnetic fields. They also arise in many diverse applications as ecology, mechanical systems, earth sciences and mathematical finance.

A derivation of methods appropriate for particular classes of PDEs will be presented. We will focus on analysis of stability, accuracy, convergence, and implementation of these methods. Students will get computational experience in applying the algorithms studied using the MATLAB problem-solving environment. We will also discuss techniques particularly efficient in solving linear systems arising from implicit discretizations of PDEs, and contrast finite difference and finite element methods, as time permits.

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. Familiarity with PDEs is a plus; however we will develop the basics as necessary. Those who have taken the equivalent of MTH452/552 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 453 will be able to:

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

• Analyze stability and accuracy properties of families of schemes
• Evaluate trade-offs of accuracy and efficiency of methods

Grade Distribution

*Note: Final exam grade will replace midterm grade if higher.

Grade Scale