Numerical Methods II, Spring 2018

Resources and source material

Suggested books

On PDE (partial differential equations) for people who have not taken a class: The Feynman Lectures on Physics. These notes by Richard Feynman cover much of basic physics in a way intended for smart people who want to understand things. It is organized into Lectures on different topics. The lectures on heat flow describe the heat equation. The lectures on wave propagation describe the wave equation. The lectures on electro-statics describe the Laplace equation.

On basic numerical analysis, including difference and integration formulas, interpolation, Richardson extrapolation, etc., Numerical Methocs by Dahlquist and Björk. This book is out of date but has the most clear descriptions of the basic operations anywhere. The second best source is Principles of Scientific Computing, course notes by Bindel and Goodman.

Lecture notes and other files

Part 1, Runge Kutta methods

Code to apply forward Euler to the Lorenz system
The pdf file (graph) you should get by running ODE_fE_Lorenz.py
Code to apply a two stage Runge Kutta method to the Lorenz system
The pdf file (graph) you should get by running ODE_trap_Lorenz.py
A zip file with the three Python modules that simulate the Fermi Pasta Ulam lattice
Three movies made using the Fermi Pasta Ulam lattice solver

Large time step, the simulation blows up before the end

Play movie in the browser

Download the movie

Medium time step, the simulation does not blow up but is not accurate either

Play movie in the browser

Download the movie

Small time step, accurate simulation but slow

Play movie in the browser

Download the movie

Code for the longer time Lorenz simulation with chaos and no accuracy
The plot you should get by running LorenzChaos.py

Part 2, discrete Fourier analysis, time dependent fields

Code to experiment with Fourier interpolation

Part 3, linear multistep methods

Part 4, hyperbolic PDE