Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 228B: Numerical Methods for Partial Differential Equations
Approved: 2011-06-02,

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
R. J. LeVeque. Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems. SIAM, 2007.
http://epubs.siam.org/doi/book/10.1137/1.9780898717839
Search by ISBN on Amazon: 978-0-89871-629-0

Course Description:

Topics Covered:
  • 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

The first two topics (about 3-4 lectures) are covered in Chapter 5-8 of LeVeque. The rest of the course are covered in chapters 9 and 10 with elements from chapter 11. Instructors might want to supplement material presented from other sources. Table of contents of the relevant chapters are attached

Programming

This class will require writing computer programs. Typically four will be assigned for the quarter. You may use any language. If you do not have a strong preference of language, it is recommended that you use MATLAB.