Modeling and Computation in Science and Engineering

ESAM 346

Winter 2007

Hermann Riecke

Tech LG62 TuTh 2-3:20

Overview of the class:

  1. Introduction
    1. Applications
    2. First Glimpse of Basic Methods
  2. One-Step Methods
    1. Taylor-Series Methods
    2. Using Quadrature
    3. Runge-Kutta Methods
  3. Error Estimate and Control of Time Step
    Foward Euler code for demo F.m
      Error Estimate and Extrapolation
    1. Adaptive Time Step
      adapt.m f.m steprkopt.m rk4.m
  4. Multi-Step Methods
    1. Adams-Bashforth Methods
    2. Adams-Moulton Methods
    3. Predictor-Corrector Methods
    4. Implementation of Implicit Methods: Newton's Method
  5. Convergence and Stability
    1. Absolute Stability
    2. Consistence, Stability, Convergence
  6. Stiff Equations
  7. Application to Partial Differential Equations
  8. Stochastic Ordinary Differential Equations
  9. Two-Point Boundary-Value Problems
Applications:
In the homework assignments the methods will be extensively applied to a variety of interesting topics in science and engineering. A brief introduction to these areas will be given in the lectures:
  1. Interacting Particles: Boids and Flocks
    For movies of swarms go to starlings or wildebeests
    For more on boids go to boids
  2. Materials: Ostwald Ripening in Deposition on Surfaces
  3. Neuroscience: Dynamics of Nerve Cells
  4. Control: Control of a Toy Robot
Assignments:
there will be 5 homeworks:

Homework 1 startup.m flock_template.m
Homework 2 F.m
Homework 3
r.h.s. for Hodgkin-Huxley model F.m
Homework 4
auxiliary functions for Newton part code:
function G for BE G_BE.m Jacobian for BE dG_BE.m
function G for BD2 G_BD2.m Jacobian for BD2 dG_BD2.m
Hodgkin-Huxley paper

Office Hours:
TuTh 3:30-4:30 in M458

David Chopp's Lecture Notes
Sketch of Lecture Notes

A copy of Tobin Driscoll's Crash Course in MATLAB can be picked up in the department office M423