CTRFlow

330T Engineering Building
Brigham Young University
Provo, UT 84602
801-422-1772
davidlignell@byu.edu

Lecture Notes

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NOTE: nbviewer.org is not rendering plots in julia. You will need to download the notebook and open it locally to see the plots.

Lectures

Class 1 Introduction

Notes (pdf)

Class 2 Errors, accuracy, and roundoff

Questions
Notes
Slides
Some good links
- Cook: What’s so hard about finding a hypotenuse?
- Cook: Math library functions that seem unnecessary
- Cook: Anatomy of a floating point number
- What every computer scientist should know about floating point arithmetic
- Base 3 is best
  - Brian Hayes, “Third Base,” American Scientist 89(6):490-494(2001).

Class 3 Linear algebra review

Class 4 Linear systems-direct methods

Class 5-6 Linear systems-iterative methods

Class 7 Nonlinear equations I

Class 8 Nonlinear equations II

Class 9 Nonlinear equations III

Class 10 Numerical derivatives

Class 11 ODEs I

Class 12 ODEs II

Class 13 ODEs III

Questions
Notes
Corresponding jupyter notebook file (right click, save as)

Class 14-15 Stability, consistency, stiffness

Class 16 BVPs: shooting methods

Class 17 BVPs: relaxation methods

Class 18 BVPs: Boundary conditions, nonlinear, nonuniform

Class 19 PDEs: introduction

Class 20 PDEs: parabolic

Class 21 PDEs: stability

Class 22 PDEs: multidimensional

Class 23 PDEs: ADI method

Class 24 PDEs: Finite volume method

Class 25 PDEs: Finite volume method 2

Class 26 PDEs: Advection and diffusion (Python)

Class 27 PDEs: Advection and diffusion II exponential scheme

Class 28 Hyperbolic equations

Class 29 projects

Class 30 projects

Class 31 Hyperbolic equations, flux limiters, Euler equations

Class 32 Integration I, Trapezoid, Simpson’s

Class 33 Integration II, adaptive, Monte Carlo

Class 34 Sample from PDF

Class 35 Gauss Quadrature