MATH 5620 (Spring 2017)

This page contains resources and schedules for Math 5620.  Please check this page on a regular basis. The documents
on this page will be regularly updated as well.

Introduction
This PDF contains basic details about this class: office hours, information about assignments, and the things we will cover over the course of the semester.

Schedule

This schedule indicates the topics we will be covering over the semester. Print out or bring the appropriate handout to class. If you must take lecture notes, do so as a supplement to the handout itself; I'd rather you listened carefully in class. I will tell you which handout to bring before each lecture.

The schedule will be updated as we progress. It is your responsibility to check the schedule.

Topic Handouts Assignment
Review I: Polynomial Interpolation Polynomial Interpolation Assignment 1 (review)
baryeven.m, barycheb2.m, chebspace2.m, Test.m
Review II: Finite Differences and Quadrature FD and quadrature
Linear Multistep Methods I: Adams and BDF methods Linear Multistep I Assignment 2 (ODEs)
AB2.m (modified from original code by Professor Greg Fasshauer), AB2TestScript.m
DUE DATE: 02/06/2017

Linear Multistep Methods II: Consistency, Stability and Convergence Linear Multistep II
Multistage Methods: Runge-Kutta Methods Multistage I
ODE Wrap-up: RK Stability, Adaptive time-stepping, IMEX Methods Multistage II
Adaptive Methods
IMEX Methods
RKStability.zip
Intro to Numerical Methods for PDEs Num. PDEs Intro. Assignment 3 (parabolic PDEs)
DUE DATE: 02/24/2017
Finite Difference Methods I: Elliptic PDEs FD Elliptic
Finite Difference Methods II: Parabolic PDEs FD Parabolic
Finite Difference Methods III: Consistency, Stability and Convergence FD Stability Assignment 4 (FD for hyperbolic PDEs, Chebyshev spectral methods for 1D heat equation)
DUE DATE: 04/11/2017
cheb.m (code to compute Chebyshev differentiation matrices)
Finite Difference Methods IV: Hyperbolic PDEs FD Hyperbolic
Spectral Collocation Methods I: Chebyshev and Fourier Pseudospectral Methods (Greg Fasshauer's notes, based on Nick Trefethen's notes)
ChebyshevAccuracyDemo.m
Radial Basis Function (RBF) Interpolation Fornberg and Flyer: Solving PDEs with RBFs
Fuselier and Wright: Global RBFs for reaction-diffusion PDEs on Surfaces
Shankar,Wright, Kirby and Fogelson: RBF-FD for reaction-diffusion PDEs on Surfaces
Bengt Fornberg's Research Page
Grady Wright's Research Page
Greg Fasshauer's Research Page
Varun Shankar's Research Page
Spectral Collocation Methods II: RBF Methods  
RBF-Finite Difference (RBF-FD) Methods
Incompressible Flow I: Saddle Point Problems Incompressible SPP ----
Incompressible Flow II: Projection Methods Brown, Cortez and Minion: Accurate Projection Methods for the Incompressible Navier Stokes Equations
Guy and Fogelson: Stability of Approximate Projection Methods on Cell-Centered Grids