Modeling and Computation in Science and Engineering

ESAM 346

Winter 2005

Hermann Riecke

Tech L158 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. Fluid Flow: Vortex Dynamics
  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 F.m Euler code

Homework 2 F.m

Homework 3 F.m G_BE.m dG_BE.m G_BD2.m dG_BD2.m
Hodgkin-Huxley paper

Homework 4

Homework 5 f.m


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

David Chopp's Lecture Notes
Sketch of Lecture Notes (in preparation, yet incomplete)

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