Schedule

  Class times: MWF 10:45-11:35 in A 226 CEB or as announced.

Predetermined dates:

• 01/13/03 HW 2.1, 2 due
• 01/15/03 HW 2.5 (assume a-f all constant), 8, 9(a) due
• 01/22/03 HW Describe typical properly posed problems for the Laplace, heat, and wave equations. Describe what the CFL condition tells us about how to solve those equations on a mesh of points.
• 01/27/03 HW 2.12 (write as ), 14
• 01/31/03 HW: Derive the exact solution of groups project 1 using the method of separation of variables. Compare with the functions exact on the web page and comment on the questions in the comments.
• 02/03/03 HW 3.2 3.16 ( and .)
• 02/05/03 Project 1 due.
• 02/07/03 For the finite difference formula , find the PDE with which this FDE is consistent and find the order of accuracy. Note: the Courant number is defined as . Use many terms in the Taylor series.
• 02/10/03 Use operators to derive a second order accurate finite difference formula for (u_xxx)_jⁿ that is as compact as possible, i.e. that only uses u values at mesh points as close as possible to j itself. Write it out both in terms of operators and in terms of mesh point values. Derive the truncation error of your formulae using Taylor series. Verify that the same truncation error is obtained from multiplying the expansions on the formula sheet.
  
  Also, use your program at N=0.5 and and 32 to examine whether the maximum error at time (i.e., about 0.5) is really as it should be. Also examine whether the error is for N=1/6. Repeat both for the case that V₁ is 1 instead of 2. Explain the results.
• 02/14/03 Use both the second order and the fourth order compact scheme to evaluate u_xx between x=0 and x=2, using . Take u=e^x. For the compact scheme, you can use the exact values of the second derivative at the end points x=0 and x=2. Is the compact scheme more accurate?
• 02/21/03 Exam I
• 02/24/03 Crank-Nicholson consistency and accuracy using Taylor series due.
• 03/05/03 HW 3.4 due.
• 03/19/03 Group project 2 due.
• 03/21/03 3.11, 17, 18, 19 due.
• 03/26/03 3.25, 26, 27 due.
• 04/02/03 Exam II
• 04/07/03 (a) Do McCormack scheme stability as stands. (b) Reduce the scheme to LW.
• 04/09/03 Derive the conservative form of the equations of axisymmetric inviscid nonconducting flow. Make sure there are no nonconservative derivative terms.
• 04/11/03 Convert coordinates and bring the equations back into conservative form.
• 04/25/03 Individual project 1 due.
• 04/30/03: Wednesday 12:00 Final Project due