APMA2811F - Notes and Codes


Below are additional notes and Matlab scripts of codes used in class

1. 9/9/09 Class
  1. Harmonic oscillator solver comparison [CODE]
  2. RK system test [CODE]

2. 9/23/09 Class
  1. Convergence of forward Euler for scalar case [CODE]
  2. Convergenve of forward Euler for system case [CODE]
  3. Visualization of system case [CODE]
  4. Special case with lower convergence [CODE]
  5. Special case with higher convergence [CODE]
  6. Forward Euler using compensated summation [CODE]

3. 9/30/09 Class
  1. Stability test for scalar forward Euler [CODE]
  2. Stability test for system forward Euler [CODE]
  3. Stability test for system backward Euler [CODE]
  4. Stability region/surface for forward Euler [CODE]
  5. Stability region/surface for backward Euler [CODE]
  6. Backward Euler solved using point iteration [CODE]
  7. Backward Euler solved using a Newton iteration [CODE]
  8. Stability region/surface for Crank-Nicholson [CODE]
  9. Stability region/surface for 2nd order ERK [CODE]
  10. Comparison of schemes for stiff problem [CODE]
  11. Stability region/surface for 2nd order Adam-Bashforth [CODE]
  12. Stability region/surface for 4th order ERK [CODE]

4. 10/7/09 Class
  1. Stability region/surface for 2nd order ERK [CODE]
  2. Stability region/surface for 3rd order ERK [CODE]
  3. Stability region/surface for 4th order ERK [CODE]
  4. Failure of simple RK order condition test [CODE]
  5. Failure of scalar/system RK order conditions [CODE]

5. 10/21/09 Class
  1. Notes on rooted trees [NOTE]
  2. Failure of simple RK order condition test [CODE]
  3. Deformation of 2nd order, 3 stage RK stability region [CODE]
  4. Adaptive ERK code with embedded error estimator [CODE]
  5. Right hand side for gravitational problem [CODE]

6. 10/28/09 Class
  1. Article on limits to stage growth of stability region [NOTE]
  2. Wikipedia page on Pade tables for the exponential [LINK]
  3. Stiff problem and order reduction [CODE]
  4. Right hand side for test problem [CODE]

7. 11/04/09 Class
  1. Stiff problem and order reduction [CODE]
  2. Right hand side for test problem [CODE]

8. 11/11/09 Class
  1. Adam-Bashforth stability regions [CODE]
  2. Adam-Moulton stability regions [CODE]
  3. BDF stability regions [CODE]

9. 11/18 Class
  1. Notes on Geometric Integration [NOTE]