Spring 2016

Policy sheet

Syllabus

Dr. Kreider's schedule

Set 2, due Thursday 4 February

Set 3, due Thursday 18 February

Set 4, due Thursday 25 February

Set 5, due Thursday 3 March

Set 6, due Thursday 31 March

Set 7, due Tuesday 12 April

Set 8, due Thursday 28 April

Set 9, due Thursday 5 May

MATLAB Overview

Mathworks Academy

Mathworks Examples

Numerical Differentiation:

ExDER1.m -- Simple Example: Euler's Method

Derivation of the 4th order central difference formula

ExDER2.m -- Comparison of O(h), O(h^2), O(h^4)

ExDER3.m -- Derivative Approximation Using LIPs

divdiff.m

newtval.m

deriv.m

lagran.m

ExDER4.m -- Effect of h on CD2

ExDER5.m -- Effect of noise on CD2

ExDER6.m -- Using the forward WENO 5th order method

Exembed.m -- example of an embedded function

symmetry.pdf -- Symmetric differentiation formulas are better

extrapolation.pdf -- Extrapolation example (using the form of error estimates)

Numerical Ordinary Differential Equations:

Ex2embeddedfunction.m -- another example of an embedded function

ExODE1.m -- Euler's Method

ExODE2.m -- Euler versus Heun - graphical

ExODE3.m -- Euler versus Heun - numerical

ExODE4.m -- Taylor's Method

ExODE5.m -- Stability: Explicit versus Implicit Euler

ExODE6.m -- Runge Kutta 2nd order versus 4th order

ExODE6a.m -- You need to know how to use the solvers

ExODE7.m -- Predictor Corrector methods versus Runge Kutta

ExODE7a.m -- ABM4 with poor start-up algorithm

ExODE8.m -- Stiff system using Euler

ExODE8b.m -- Stiff system using ode23s

ExODE9.m -- Shooting method for a BVP, linear problem

ExODE10.m -- Shooting method for a BVP, nonlinear problem

ExODE11.m -- Numerical convergence, grid refinement

ExODE12.m -- Using MATLAB solvers, scalar equation

ExODE13.m -- Using MATLAB solvers, system of equations

projectile.m -- modeling application: 2d projectile motion

trinumrec.m -- tridiagonal solver

ExBVP.m -- Using bvp4c, boundary value problem solver

duffing.m -- analysis of Duffing's equation

ExCreviceStrippedDown.m -- Crevice Corrosion using bvp4c

ExODEscaling.m -- Working with scaled variables

ExODEparam1.m -- using nested functions to provide parameters

ExODEparam2.m -- using function handles to provide parameters

ExODEparam3.m -- using global variables to provide parameters

fparam.m -- the function that accepts the global variables

Numerical Solution of Partial Differential Equations:

ExPDE1.m -- Visualization with movies

ExPDE2.m -- Visualization with 2d cross sections and 3d surfaces

ExPDE3.m -- Visualization: surface plot options

stability.pdf -- von Neumann stability analysis

ExPDE4.m -- Parabolic PDE: classic vs Richardson, stable vs unstable

savememory.pdf -- Notes on saving memory

findtypo.pdf -- Notes on programming style

ExPDE5.m -- Parabolic PDE: the effect of convection

tridiag.m -- tridiagonal solver

ExPDE6.m -- Parabolic PDE: Crank-Nicolson is stable and fast

Summary of Parabolic Algorithms

ExPDE20.m -- what does diffusion look like?

ExPDE21.m -- what does convection look like?

ExPDE22.m -- what does a source look like?

ExPDE23.m -- what do the various boundary conditions look like?

ExPDE24.m -- Crank-Nicolson for an elliptic PDE

ExPDE7.m -- Elliptic PDE: the maximum principle

ExPDE8.m -- Elliptic PDE: the effect of a single typo

ExPDE9.m -- Elliptic PDE: SOR iteration dirich.m

ExPDE10.m -- Hyperbolic PDE: traveling waves and superposition principle ExPDE11.m -- Hyperbolic PDE: Advection Equation

ExPDE12.m -- Hyperbolic PDE: Wave Equation (with only numerical dispersion and dissipation)

ExPDE13.m -- Hyperbolic PDE: Klein-Gordon Equation (with physical dispersion)

ExPDE14.m -- Hyperbolic PDE: Lax Friedrichs for a conservation law

MUSCL beats Lax-Wendroff

Lax-Wendroff with smooth profile

Lax-Wendroff with discontinuous profile (embedded functions)

Lax-Wendroff with artifacts

von Neumann stability analysis