Numerical Methods for PDEs (Math 566)
This course will introduce you to methods for solving partial differential equations (PDEs) using finite difference methods. The course content is roughly as follows :
 Numerical time stepping methods for ordinary differential equations, including forward Euler, backward Euler, and multistep and multistage (e.g. RungeKutta) methods.
 Steadystate diffusion equation (an elliptic PDE), with particular emphasis on the numerical linear algebra techniques needed to solve the resulting discrete system, i.e. sparse direct methods such as tridiagonal solvers, and iterative methods, including Jacobi Method, GaussSeidel and conjugate gradient.
 The time dependent heat equation (an example of a parabolic PDE), with particular focus on how to treat the stiffness inherent in parabolic PDEs. We will consider implicit methods such as CrankNicolson, as well as stable explicit methods such as RungeKutta Chebyschev methods.
 Numerical methods for PDEs describing transport of species, seismic waves, and other physical phenomena naturally described by wavelike motion. Such PDEs are examples of hyperbolic PDEs. We will focus mainly on linear problems, but if there is interest, we can also consider nonlinear hyperbolic equations.
 Basic course information
 Required and suggested textbooks
 Lectures
 Homework Assignments
 Final Project
 Matlab tutorials
 Grading policy
Send me an email
Please send me an email at donnacalhoun@boisestate.edu so that I can compile an email list for the class. At the very least, include a subject header that says "Math 566". You may leave the message area blank, if you wish, or send me a short note about what you hope to get out of this course.
Basic course information
Instructor  Prof. Donna Calhoun 
Time  Monday/Wednesday 3:004:15 
Place  MG 124 
Office Hours  TBA 
Prerequesites  Math 465/565 or permission of instructor 
Required and suggested textbooks
 Finite Difference Methods for Ordinary and Partial Differenial Equations (Time dependent and steady state problems), by R. J. LeVeque. Society for Industrial and Applied Mathematics (SIAM), (2007) (required).
 A Friendly Introduction to Numerical Analysis, by Brian Bradie. Pearson Prentice Hall, (2006) (suggested).
 Analysis of Numerial Methods, by Eugene Isaacson and Herbert Keller. Dover Books on Mathematics, (1994) (suggested).
 Numerical Computing with Matlab, by Cleve Moler. Mathworks, Inc., (2004) (suggested).
 Learning Matlab, by Toby A. Driscoll. The Society for Industrial and Applied Mathematics, (2009) (suggested).
Lectures
Week #1 (Jan. 22) 
Wednesday 
Three basic PDE types

Week #2 (Jan. 27) 
Monday 
Chapter 1 : Finite Difference Approximations (Sec. 1.11.3)
Wednesday 
Chapter 1 : Finite Difference Approximations (Sec. 1.41.5)

Week #3 (Feb. 3) 
Monday 
Chapter 2 : Steady State and Boundary Value Problems (Sec. 2.12.3)
Wednesday 
Chapter 2 : Steady State and Boundary Value Problems (Sec. 2.42.6)

Week #4 (Feb. 10) 
Monday 
Chapter 2 : Steady State and Boundary Value Problems (Sec. 2.72.9)
Wednesday 
Chapter 3 : Elliptic Equations (Sec. 3.13.4)

Week #5 (Feb. 17) 
Monday 
President's Day
Wednesday 
Chapter 4 : Iterative Methods for sparse Linear Systems (Sec. 4.14.2

Week #6 (Feb. 24) 
Monday 
Chapter 4 : Iterative Methods for Sparse Linear Systems (Sec. 4.34.4)
Wednesday 
Chapter 5 : Initial Value Problems (Sec. 5.15.3)

Week #7 (Mar. 3) 
Monday 
Chapter 5 : Initial Value Problems (Sec. 5.45.6)
Wednesday 
Chapter 5 : Initial Value Problems (Sec. 5.75.9)

Week #8 (Mar. 10) 
Monday 
Chapter 6 : Zerostability and Convergence for
Initial Value Problems (Sec. 6.16.2)
Wednesday 
Chapter 6 : Stability of Euler's Method
(Sec. 6.36.4)

Week #9 (Mar. 17) 
Monday 
Chapter 6: Stabilty of nonlinear methods; connection to BVP (Section 6.3)
Wednesday 
Review of linear multistep methods; Zerostability of LMM (Section 5.9; 6.4)

Week #10 (Mar. 31 ) 
Monday 
Chapter 7 : Absolute Stability for Ordinary Differential Equations (Sec. 7.17.3)
Wednesday 
Chapter 7 : Absolute Stability for Ordinary Differential Equations (Sec. 7.47.6)

Week #11 (Apr. 7) 
Monday 
Chapter 8 : Stiff Ordinary Differential Equations (Sec. 8.18.3)
Wednesday 
Chapter 8 : Stiff Ordinary Differential Equations (Sec. 8.48.6)

Week #12 (Apr. 14) 
Monday 
Chapter 9 : Diffusion Equations and Parabolic Problems (Sec. 9.19.4)
Wednesday 
Chapter 9 : Diffusion Equations and Parabolic Problems (Sec. 9.59.7)

Week #13 (Apr. 21) 
Monday 
Solving parabolic equations; Lstability
Wednesday 
Chapter 10 : Advection Equations and Hyperbolic Systems (Sec. 10.110.2)

Week #14 (Apr. 28) 
Monday 
Chapter 10 : Advection Equations and Hyperbolic Systems (Sec. 10.3)
Wednesday 
Chapter 10 : Advection Equations and Hyperbolic Systems (Sec. 10.310.4)

Week #15 (May 5) 
Monday 
Chapter 10 : Advection Equations and Hyperbolic Systems (Sec. 10.410.5)
Wednesday 
Chapter 11 : Mixed Equations (Sec. 11.111.3)

Homework Assignments
Homework projects are designed to enforce mathematical concepts discussed in class.
Homework #1 
Due Feb. 26

Homework #2 
Due April 4th

Homework #3 
Due April 9th

Homework #4 
Due April 28th

Homework #5 
Due May 9th

Final Project
In lieu of a final, you will have a final project due, on the day of our scheduled exam. Please turn in a 12 page project proposal by the end of week 10. A 510 page writeup of your project will be due during the week of finals.
Matlab tutorials
Below are a series of tutorials that should help you become familar with Matlab syntax
Grading policy
Homeworks will count for 75% of your final grade, and a final project will count towards 25% of your final grade.