# AMath 585: Numerical Analysis of Boundary Value Problems SLN 10259A, MWF 3:00-3:50, Loew Hall 206

 Instructor: Professor Loyce M. Adams Office: Lewis 306 Tel: 543-5077 Fax: 685-1440 Email: lma3 AT uw DOT edu Office hours: MWF 4:00-5:00 or by appt. TA: Teaching Assistant: Yian Ma Office: Lewis 129 Tel: Fax: Email: yianma at uw dot edu Office hours: Tuesday 12-2

 Homework Grades Other Resources 2013 Web Page

 Catalyst Page EDGE Video Page Course description Textbook Syllabus Objectives Schedule

## Catalyst WEB Page for AMATH585

Your homework will be submitted via the Homework Dropbox on the class Catalyst Page. Your written homework should be typed via Latex or some typesetting program that can be converted to .pdf format. Computer programs done in Matlab may graded by running them to check the output is correct. They will also be checked for good programming and numerical analysis practices. An analysis of the code's results as requested in the assignment will be submitted via the .pdf file to the Homework Dropbox. A goal of this course is for you to learn to analyze your computer results. You should be able to access the Catalyst site with your UW netid.

## EDGE Streaming Video WEB Page for AMATH585

The course is recorded by EDGE. You may watch the lectures by going to the link below:

## Course Description

Numerical methods for steady-state differential equations. Two-point boundary value problems and elliptic equations. Iterative methods for sparse linear systems: conjugate-gradients, preconditioners, and multigrid. (This course is offered every Winter quarter. This quarter it is an EDGE course.)

## Syllabus (and tentative schedule)

• Chapter 1. Finite difference approximations (2 lectures)
• Chapter 2. Two-point boundary value problems for ODEs (3 weeks)
• Character of solution; boundary conditions.
• Finite difference method for linear problem u'' = f, BCs at x = 0,1.
• Accuracy, convergence, stability.
• Finite difference methods for nonlinear problems
• Boundary layers and nonuniform grids
• Chapter 3. Elliptic Equations (3 weeks)
• Laplace/Poisson equation - some physical examples
• Finite difference method; solution via Gaussian elimination.
• Fast Poisson solvers using FFT.
• Chapter 4. Iterative Methods for Sparse Linear Systems (2 weeks)
• Jacobi, Gauss-Seidel, SOR
• Methods for nonsymmetric systems
• Multigrid methods

## Learning Objectives and Instructor Expectations

The course will be a combination of computation and theoretical analysis. The goal is to obtain an understanding of numerical methods and their implementation, as well as learning mathematical techniques for analyzing the stability and accuracy of these methods.

There will be homework assignments roughly bi-weekly that will involve MATLAB programming and written exercises. You may consult with your classmates about how to do the homework, but you should write your own code and express the answers to the written questions in your own words. Any sources you use should be referenced.

## Schedule and Homework

The homework will be assigned on the Catalyst Web site.