3450:428/528 Applied Numerical Methods II
Spring 2012


Policy sheet
Syllabus

Homework Sets

Set 1, due Thursday 2 February
Set 2, due Thursday 9 February
Set 3, due Thursday 16 February
Set 4, due Thursday 1 March
Set 5, due Tuesday 27 March
Set 6, due Tuesday 10 April
Set 7, due Thursday 26 April

Computer Projects

Project 1 -- Using functions in MATLAB, due Tuesday 31 January
Project 2 -- Computational Efficiency and Numerical Convergence, due Tuesday 21 February
Project 3 -- Crevice Corrosion, due Tuesday 6 March
Project 4 -- Crank-Nicolson, due Thursday 5 April
Project 5 -- SOR Method, due Thursday 19 April

Downloads

Background information on MATLAB:
MATLAB Overview
Website with modules associated with the text

Numerical Differentiation:
ExDER1.m -- Euler's Method
Derivation of the 4th order central difference formula
ExDER2.m -- Central Difference Error
ExDER3.m -- Derivative Approximation Using LIPs
    divdiff.m
    newtval.m
    deriv.m
    lagran.m
symmetry.pdf -- Symmetric differentiation formulas are better
extrapolation.pdf -- Extrapolation example (using the form of error estimates)
LIP.pdf -- Lagrange Interpolation: irregular grid
ExDER4.pdf -- Differentiating a boundary condition for a PDE
 
Numerical Ordinary Differential Equations:
ExODE1.m -- Euler's Method
ExODE2.m -- Euler versus Heun
ExODE3.m -- Euler versus Heun Error
ExODE4.m -- Taylor's Method
ExODE5.m -- Stability: Explicit versus Implicit Euler
ExODE6.m -- Runge Kutta 2nd order versus 4th order
ExODE7.m -- Predictor Corrector methods versus Runge Kutta
ExODE8.m -- Stiff system
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
trinumrec.m -- tridiagonal solver
ExBVP.m -- Using bvp4c, boundary value problem solver
duffing.m -- analysis of Duffing's equation
 
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
ExPDE4.m -- Parabolic PDE: classic vs Richardson, stable vs unstable
ExPDE5.m -- Parabolic PDE: the effect of convection
tridiag.m -- tridiagonal solver
ExPDE6.m -- Parabolic PDE: Crank-Nicolson is stable and fast
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