M612-010 Introduction To Numerical Methods for Partial Differential Equations
Spring 2008
General Information
MWF 11:15-12:05 am (EWG 209)
www.math.udel.edu/~hsiao

• Instructor: Professor George C. Hsiao
• Office: Ewing 528 (Tel: 831-1882): E-mail: hsiao@math.udel.edu
• Office Hours: MW 3:30-5:00 pm and by appointment.
• Homework and Computer Projects:
  (a) Problem assignments will be given regularly during the semester and will be collected from time to time.
  (b) Two or three computer projects will be assigned and will also be collected.
• Grading: Course grade will be computed according to the following formula:
  (a) Homework: 60 %
  (c) Computer Projects: 40%

Syllabus

General description: This course is particularly designed for students in applied mathematics, physical sciences, and engineering. It introduces to the students the basic concepts of consistency, convergence and stability of difference schemes for the numerical treatment of partial differential equations in physical applications. Theoretical results of partial differential equations will be used as motivations for developing the analogous results for difference equations. Emphasis will be placed on the interpretation and understanding of the numerical methods and their generalizations, so that students can apply these methods to their own specific problems. The general computer programming language for the course is MATLAB.

Topics to be covered:
(I) Finite Difference Methods: Introduction; General concepts: consistency, convergence and stability; Application to a two-dimensional Dirichlet problem in a closed bounded domain.
(II) Cauchy Problems: Application of explicit difference scheme to the wave equation, domain of dependence, Courant-Friedrichs-Lewy condition, von Neumann stability criterion, error propagation, convergence of difference solutions.
(III) Initial-Boundary Value Problems: Explicit and implicit schemes for the parabolic equation; Method of lines; Error estimates and stability conditions; method of solutions of the difference equation for the implicit scheme.
(IV) Selected Topics: Simple model problems in elasticity and fluid mechanics will be used for introducing other modern numerical schemes in practice.

Text: K.W. Morton and D.F. Mayers: Numerical Solution of Partial Differential Equations, 2nd Edition, Cambridge 2005.

Classical References: E. Isaacson and H. B. Keller: Analysis of Numerical methods, John Wily& Sons, Inc. 1966.
G. E. Forsythe and W. R. Wasow: Finte-difference Methods for Partial Differential Equations, John Wily & Sons, Inc. 1967.

Additional Reference: A. Quarteroni and A. Valli: Numerical Approximation of Partial Differential Equations, Springer, 1994