AMATH 586
SLN 1198, MWF 12:30-1:20, Loew Hall 101

Approximate and Numerical Analysis III

Instructor:

Professor Randall J. LeVeque
Guggenheim 408A
tel: 685-3037
fax: 685-1440
rjl@amath.washington.edu
office hours: MW 1:30-3:30

Homework

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2001 Web Page

Course description

Textbook

Syllabus

Objectives

Schedule

Course Description

Finite-difference methods for time-dependent differential equations. Multistep methods, stiff equations, implicit methods. Hyperbolic and parabolic partial differential equations. Stability and convergence theory.

Prerequisites

AMath 581 or AMATH 584

Syllabus

The main topic is finite difference methods for time-dependent differential equations.

Review of numerical methods for ODEs (initial value problems)
- Consistency, convergence
- Zero stability and absolute stability, stability regions
- Linear multistep and Runge-Kutta methods
- Stiff problems, BDF methods
- Software
Numerical Methods for time-dependent partial differential equations
- Hyperbolic and parabolic equations
- Explicit and implicit methods
- Lax-Richtmyer stability, von Neumann analysis
- Method of lines approach, relation to stiff ODEs
- Finite volume methods
- Introduction to shock capturing methods, flux limiters
- Spectral and pseudospectral methods
- Convection-diffusion and reaction-diffusion equations

Textbook

Course Notes for 585-6 by R.J. LeVeque
- The first installment contains material on methods for ODEs and will be used during the first two weeks of class:
  586part1.ps ... 586part1.pdf
- Chapters 2--5 were covered in AMath 585. These chapters are available here if you did not get them last quarter and want to see this material:
  585chapters.ps ... 585chapters.pdf
- The second installment of 586 notes, Chapters 9-13:
  586part2.ps ... 586part2.pdf
- The third installment of 586 notes, Chapter 14:
  586part3.ps ... 586part3.pdf
- The fourth installment of 586 notes, Chapter 15-17:
  586part4.ps ... 586part4.pdf

Other references:

On reserve in the Engineering Library:
- J. D. Lambert, Numerical methods for ordinary differential systems: the initial value problem, Wiley, 1991.
- A. Iserles. Numerical Analysis of Differential Equations. Cambridge University Press, 1996.
- J. C. Strikwerda, Finite difference schemes and partial differential equations, Wadsworth & Brooks/Cole, 1989.

Assignments

Follow links in the table below to obtain a copy of the homework in PostScript (.ps) or

Adobe Acrobat (.pdf) format. You may also obtain here solutions to some of the homework and exam problems. An item shown below in plain text is not yet available. For additional information regarding viewing and printing the homework and solution sets, click here.

Tentative Schedule

	Date	Event	Homework Problem Sets
Week 1	M, April 1	First day of classes
Week 2	F, April 12	Homework 1 due	hw1.ps ... hw1.pdf
Week 5	M, April 29	Homework 2 due	hw2.ps ... hw2.pdf
Week 7	Monday, May 13	Homework 3 due	hw3
Week 7	F, May 17	Midterm
Week 9	M, May 27	Memorial Day
	W, May 29	Homework 4 due	hw4
Week 10	F, June 7	Last class
Finals week	W, June 12	Final project due	.ps ... .pdf

Grading

Please take a look at the handout below for some hints on writing up homework solutions.

Format for homework solutions and a sample write-up ... hw0.ps ... hw0.pdf
Matlab m-files to go with hw0

You may view your homework and exam grades on-line. Before doing so for the first time, you must request a password.

Tutorials

No on-line tutorials have been assigned for AMATH 586.

Approximate and Numerical Analysis III

Instructor:

Course Description

Prerequisites

Syllabus

Textbook

Other references:

Assignments

Tentative Schedule

Grading

Tutorials

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