Course Outline

We will cover the following topics, roughly in the order given: Difference approximation of spatial derivatives, truncation error, Fourier analysis on the numerical grid, time differencing, model explicit schemes for the advection equation, accuracy analysis, consistency, stability, convergence, numerical dispersion and dissipation, model implicit schemes, initial boundary value problems for time dependent partial differential equations, systems of partial differential equations, two-dimensional problems.

The following chapters of the textbook will accompany us in the journey:

Chapter 1: Introduction to Finite Differences, Explicit Differences, Compact Differences.

Chapter 2: Consistency+Stability  ==> Convergence, The Lax Theorem.

Chapter 3: Stability Analysis of Finite Difference Schemes.

Chapter 5: Finite Difference Schemes for Hyperbolic Equations.

Chapter 7: Numerical Dispersion and Dissipation.

Chapter 6: Systems of Partial Differential Equations and Two-Dimensional Problems.

Exams

There will be one mid-term exam on October 25, 2001, during the class period.

Homework/Computational Projects

Homework will be assigned regularly. Some (or all) of the homework problems in each assignment will require computer programming, use of graphics packages, and the presentation of tabulated data obtained from the computer program. You are free to use any programming language you like, but note I can only help you with Fortran and Matlab. There are many graphics packages on our systems, if you can't pick one yourself ask me for suggestions. There will be one major computational project, assigned at the time of the mid-term exam and collected on the last day of classes. A completed project will be in the form of a research paper (details of the structure to be given later). Your ability to complete the project will depend on your having done all the programming assignments in the homework sets.

Grading

The mid-term exam will account for 25% of the course grade. The homework assignments will account for 40% of the course grade. The computational project will account for the remaining 35% of the course grade.

Library Reserve Materials

A copy of the textbook, and the book Finite Difference Schemes and Partial Differential Equations (by J. C. Strikwerda), have been placed on reserve for in-library use by students of MATH712. Other course-related materials will be placed on reserve at later dates (course notes, etc.).

Course Web Page

The course web page (always under construction !) at http://www-ec.njit.edu/~peterp/712.html contains homework assignments, computational assignments, and anything else the instructor wants the students to know about. Please check this page often for new material.