Monday 
Wednesday 
Friday 
Sept 22 
Sept 24 Autumn Classes Begin
Introduction: finite difference methods for PDEs

Sept 26 An explicit method of solution for parabolic equation

Sept 29
PDE to ODEs (Method of Lines)
Stability, Consistency, and Convergence
heat_eqn_explicit.m

Oct 1 CrankNicolson implicit method
Oct 2 EA295 2:30pm: Alexander Kurganov gives a talk in Applied Seminar
"Fast Explicit Operator Splitting Method for ConvectionDominated Problems"

Oct 3
Weighted Average Method

Oct 6
Boundary Condition and Gerschgorin's theorem on bounds for eigenvalues
HW1

Oct 8
Fourier Analysis and Von Neumann's method

Oct 10
No class today (meeting in Minneapolis)
Last day to drop without a "W"

Oct 13
Von Neumann Analysis on single step methods:
explicit, CrankNicolson

Oct 15
Von Neumann Analysis on multistep methods:
leapfrog, DufortFrankel Method

Oct 17
Matrix method for multistep methods

Oct 20
ADI method for higher dimensional heat equation
HW2

Oct 22
Operator Splitting method

Oct 24
Heat equation on circular domain

Oct 27
Miscellaneous methods for improving accuracy
Increase stencil points; generate higher order by using truncation error information

Oct 29
Miscellaneous methods for improving accuracy
Multistep method to increase accuracy in time; Richardson's correction approach

Oct 31
Nonlinear parabolic equations
Newton's method

Nov 3
HW3
Midterm: 12:30pm1:18pm

Nov 5
discuss midterm solution
Nonlinear parabolic equations
Richtmyer's linearization method

Nov 7
Richtmyer's linearization method, conti
Lee's method

Nov 10
finite difference method for elliptic equation
truncation error, order of accuracy

Nov 12 Two dimensional problem 
Nov 14
Discrete Maximal Principle; Consistency, Stability, Convergence for Elliptic Problems 
Nov 17
Iterative Methods for Solving large linear systems of algebraic equations
A necessary and sufficient condition for the convergence of iterative methods
HW4

Nov 19 Rate of Convergence 
Nov 21 Methods for accelerating the convergence of iterative process 
Nov 24
Optimum Acceleration parameter for the SOR method

Nov 26 Relationship between the eigenvalues of the Jacobi and SOR iteration matrices to a block tridiagonal coefficient matrix 
Nov 28 No Classes 
Dec 1
HW5
2 cyclic matrices

Dec 3iFinal Project 2 cyclic matrices thm applied to Poisson's equation 
Dec 5
Fast solver for Poisson Equations

Dec 8 Final Exams: 11:30am1:18pm 
Dec 10 
Dec 12 