3450:428/528 Applied Numerical Methods II
Spring 2016


Policy sheet
Syllabus
Dr. Kreider's schedule

Homework Sets

Set 1, due Tuesday 26 January
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

Downloads

Background information on MATLAB:
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