# Modeling and Computation in Science and
Engineering

## ESAM 346

### Winter 2005

### Hermann Riecke

### Tech L158 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:
- Fluid Flow: Vortex Dynamics
- 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 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