Course Annoucement

AMSC 612: Numerical Methods in Partial Differential Equations

Fall Semester, 2002
Section 0101, MWF 1:00 pm - 1:50 pm, Math 0104

Instructor: Bo Li
 Office: Math 4304; Phone: 405-5088; E-mail: bli@math.umd.edu


Partial differential equations (PDEs) are the most important continuum models in mathematical, physical, and biological sciences. Often, they can only be solved by numerical methods. The knowledge of such methods in PDEs is therefore essential to modern researches in applied mathematics as well as science and technology.

In this course, we will study the basic concepts and principles in developing accurate, reliable, and efficient numerical algorithms for PDEs, and in analyzing the stability and convergence rate for such algorithms. We will also design numerical methods for problems arising from fluid dynamics, materials science, and other areas of application.

We will mainly study finite difference methods, and spectral methods. There will be a few homework assignments but no exams. Homework problems will be both analytical and computational. But programming skills will be minimized. In addition to lectures, we will have discussions, problem solving sessions, and other actitivities.

Prerequisites:   Calculus and linear algebra. A basic knowledge of numerical analysis (e.g., AMSC 460 or AMSC 466) and PDEs (e.g., MATH 462) will be helpful but not crutial.

Textbooks:   No single textbook will be used. But the following will be the main references.

  1. Numerical Solution of Partial Differential Equations, by K. W. Morton and D. F. Mayers, Cambridge University Press, 1994.
  2. Numerical Analysis of Spectral Methods: Theory and Applications, by D. Gottlieb and S. A. Orszag, SIAM, 1977.

Grading:   Based on a few homework assignments.

Class web page:   http://www.math.umd.edu/~bli/teaching/amsc612f02/

Tentative topics:

  1. Finite difference methods for linear parabolic, hyperbolic, and elliptic equations.
  2. Consistency, convergence, and stability. Fourier analysis. Energy methods.
  3. Spectral methods for time-dependent problems and their convergence analysis.
  4. Finite difference methods for conservation laws and Hamilton-Jacobi euqations.
  5. Numerical methods for interface problems in fluids, crystal growth, etc.


Feel free to contact the instructor if you have any questions.