Math 228B

Numerical Methods for PDEs

Windter Quarter 2017

Numerical Methods for PDEs

Windter Quarter 2017

Instructor: Office: Email: Phone: Office Hours: |
Professor Bob Guy MSB 2136 guy@math.ucdavis.edu 754-9201 Monday 4-5; Friday 3-4 |

Textbook: |
R. J. LeVeque. Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems. SIAM, 2007. |

Webpage: |
http://www.math.ucdavis.edu/~guy/teaching/228b/ Homework and announcements will be posted here. |

Class: |
MWF 2:10-3:00 in BAINER 1134 |

TA: Office: Email: Office Hours: |
Jonathan Robey MSB 2229 jrobey@math.ucdavis.edu Wednesday 3:00-5:00 PM |

Homework

You are encouraged to talk with your classmates about homework problems. However, you must do your own write-up and write your own codes. All aspects of your write up must be clearly presented. Your writing should be clear and grammatically correct. Your codes must be thoroughly commented. All tables and figures must be appropriately labeled. You will be graded on the quality of your presentation.

Homework 1, due Wednesday, February 1st

Homework 2, due Friday, February 17st

Homework 3, due Friday, March 3rd

Homework 4, due Wednesday, March 15th

Homework 5, due Friday, March 24th

What we will cover

This coarse is part of the sequence 228A-C on numerical methods for partial differential equations. The second quarter (228B) will focus on time dependent problems. The topics we will cover this quarter are listed below.

- Introduction (Fourier transforms, derivation of conservation
laws, parabolic and hyperbolic PDEs)

- Numerical ODEs (briefly)

- Stability, accuracy, and convergence

- Von Neumann analysis

- Diffusion (reaction-diffusion) equation in multiple dimensions

- Nonrectangular geometry (logically quadrilateral grids and embedded grids)
- Methods for advection equation in 1D
- Dissipation and dispersion, modified equations
- Hyperbolic conservation laws
- Godunov method, wave propagation, and high-resolution methods

Your grade will be based on your homework assignments. We will likely have 4 or 5 homework assignments during this quarter.

Programming

This class will require writing computer programs. You may use any language. If you do not have a strong preference of language, it is recommended that you use MATLAB, because it is easy to use and very powerful. All codes will be turned in and must be thoroughly commented.