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 |
|
| 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 |