# Modeling and Computation in Science and
Engineering

## ESAM 346

### Winter 2007

### Hermann Riecke

### Tech LG62 TuTh 2-3:20

**Overview of the class:**

- Introduction
- Applications
- First Glimpse of Basic Methods

- One-Step Methods
- Taylor-Series Methods
- Using Quadrature
- Runge-Kutta Methods

- Error Estimate and Control of Time Step

Foward Euler code for demo
F.m
Error Estimate and Extrapolation
- Adaptive Time Step

adapt.m
f.m
steprkopt.m
rk4.m

- Multi-Step Methods
- Adams-Bashforth Methods
- Adams-Moulton Methods
- Predictor-Corrector Methods
- Implementation of Implicit Methods: Newton's Method

- Convergence and Stability
- Absolute Stability
- Consistence, Stability, Convergence

- Stiff Equations
- Application to Partial Differential Equations
- Stochastic Ordinary Differential Equations
- 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:
- Interacting Particles: Boids and Flocks

For movies of swarms go to starlings
or wildebeests

For more on boids go to boids
- Materials: Ostwald Ripening in Deposition on Surfaces
- Neuroscience: Dynamics of Nerve Cells
- 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