|
|
| Assignments and schedule |
|---|
(1-2) 1/7-9: Introduction, review of ODEs and well-posedness. Read 5.1,5.2
HW 1 due Friday, 1/18.
(3) 1/11. Difference approximations to derivatives.
(4) 1/14 at class time: meeting in
MLC computer lab for a
special "Introduction to MATLAB for ODEs" lab.
(5) 1/16: Finish Chapter 1. Richardson's extrapolation.
Start 5.3-5.6 (simple numerical methods for solving ODEs): consistency, local truncation error, global error.
(6) 1/18: FE, BE, midpoint and trapezoidal methods.
(7) 1/23: Heun (improved Euler or explicit midpoint), explicit trapezoidal methods.
Error for non-autonomous case.
HW 2 due Friday, 2/1.
Note: correction has been made. Use only lambda=-5 in Pbm.3
(8) 1/25 Runge-Kutta methods and Butcher tableaus. Error estimation using
time step doubling and higher order methods.
(9-11) 1/28-30,2/1 Multistep methods. LMM methods and their characteristic polynomials,
and necessary conditions for consistency. Worksheet on RK methods and Butcher tableau.
2/4 Class cancelled due to illness. We will make up that class meeting.
(12) 2/6. Review for exam: you can use the following problems:
5.1-3. 5.9, 5.10, 5.11, 5.13 first part., 5.15-16. Review and fill
details, if relevant, of all class examples.
On the exam (this Friday, 2/8, in class)
no notes, books, or caclulators will be allowed.
(13) 2/8 EXAM
(14) 2/11 Discrete Gronwall's lemma and global error. Convergence for FE.
(15) 2/13 Zero-stability for one-step and LMM methods. Root condition.
Dahlquist theorem: read Chapter 6.
HW due 2/25:
452: 6.1, 6.6a-b,
552: 6.2, 6.6a-c, 6.7,
All: implement BE and FE for harmonic oscillator set up as a system (see HW 1). Comment on
performance of both methods. Extra: implement trapezoidal method and comment.
All: solve all other problems 6.1-6.8 but do not turn them in.
All: Plot the following regions in complex plane: |z|<2, |z-i|>2, | |z| - i| <=1, | |z| -i| < sqrt(5)
(16) 2/15: Introduce absolute stability for FE, BE.
(17) 2/18: Discuss abs. stability for Trapezoidal method. Harmonic oscillator example.
(18) 2/20: How to plot abs. stability regions, examples with AM, AB, and TR-BDF2 methods.
Review: 7.1-7.6.
(19) 2/22: Growth factors and BDF methods. Example of chemical kinetics (Chapter 8).
(20) 2/25 Stiff problems, systems and L-stability. Summary of time-stepping for IVP.
(21) 2/27: start Chapter 2 (BVP). Examples of (non)existence, (non)uniqueness
for various booundary conditions (Dircihlet, eumann, Robin, periodic, Sturm-Liouville
theory.
(22) 2/29: Discretization of -u''=f with Dirichlet boundary conditions. LTE of
the difference approximation.
(23-25) 3/3-7: Stability and globar error measured in different norms for -u''=f.
3/10, 3/12: no class today.
3/13 THURSDAY: review and problem solving session 2:00pm-5:00pm in BEXL 211 or TBA.
(If you can only come for part of this review session, be sure to be
there between 3:00-4:00 for work using worksheets and review sheets).
HW due on the date of the Final Exam:
452: 7.3, 2.1 or 2.3, 2.2 or 2.4
552: 7.1, 7.3, 2.2, 2.5
Extras for all: solve 8.2, all from Chapter 2. Do not turn them in unless for extra credit.
3/14: Review and problem solving.
|
|
