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Lectures
Class 1 Introduction
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
Class 36 Interpolation
Class 37 Curve fitting
Class 38 Spectral methods
Class 39 Homotopy continuation
- Homotopy continuation
- Papers
- Wayburn, Seader, 1987 Homotopy continuation methods for computer-aided process design.
- Kuno, Seader, 1988 Computing all real solutions to systems of nonlinear equations with a global fixed-point homotopy.
- Khaleghi, Jalali, 2007 Multiple solutions in stability analysis using homotopy continuation in complex space.
- Rahimian, Jalali, Seader, White, 2011 A new homotopy for seeking all real roots of a nonlinear equation.
- Jimenez-Islas, Martinez-Gonzalez, Navarrete-Bolanos, Botello-Alvarez Oliveros-Munos, 2013 Nonlinear Homotopic continuation methods: a chemical engineering perspective review.