# Numerical solution of partial differential equations MTH 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!

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### Course Description

Catalog Description: Numerical solution of boundary value problems and initial-boundary value problems using finite difference and finite element methods. Analysis of stability, accuracy, and implementation of methods. Credits: 3

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
A successful student in MTH 553 will additionally be able to:
• Analyze stability and accuracy properties of families of schemes
• Evaluate trade-offs of accuracy and efficiency of methods

### Matlab

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:

### Grades

#### Grade Distribution

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

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

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

### Exams

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

### Links

Last updated: Fri Mar 26 10:41:26 PDT 2021