PHYS 305: Computational Physics II

Topics

1. Review
   • General information
   • Review of basic C programming
     • see Kernighan & Ritchie, Chapter 1
     • see the C Language Tutorial
   • Plotting graphs using plot_data and simple_plot (test programs 1, 2)
   
   
2. Some ``warm-up'' programming exercises
   
   
   • Summing a series: sine.c, sine1.c
   • Practice with functions: sine2.c, sine2a.c, sine3.c
   • Some simple function examples
   • Numerical integration
   • Numerical differentiation
   • Homework #1
   
   
3. Numerical integration of ordinary differential equations
   
   
   • Initial-value problems
   • Integration of Newton's equations of motion

     • A simple integration scheme (predict0.c, predict.c)
     • Sample predictor-corrector program
       
     • Side-by-side comparison of the second-order predictor and predictor-corrector methods

     • Homework #2

     • Time reversibility of the predictor-corrector scheme

     • The "Leapfrog" method (see simple_leapfrog.c)
     
     
   • Some standard integration schemes
     • The Euler and Mid-point methods
     • Programming example: scalar and vector versions of the Midpoint method.
     • Fourth-order Runge-Kutta integrator
     
     
   • Side-by-side comparison of first-order and second-order methods
     
     
   • In-class exercises, January 24
   • Homework #3
     
     
   • Applications
     • Chaotic scattering
     • Homework #4
       
       
     • Orbital resonances and stability
   
   
4. The driven pendulum
   
   
   • Undamped oscillations
   • Damped oscillations
   • Damped, driven oscillations
   • Visualizing the motion: pendulum_plot.c
   • Trajectories in phase space; attractors
   
   
5. Visualizing chaotic systems
   
   
   • Phase portraits and Poincare sections (handout)
   • Homework #5
     
     
   • Attractors and basins of attraction
   • Displaying 2-D data as images: (examples)
   • Homework #6
     
     

Projects (due 3/13/2002 -- choose only one!)

1. Bifurcation diagrams
2. The three-body problem

Solutions to homeworks

1. Homework #1
2. Homework #2
3. Homework #3
4. Homework #4