Problem 26   		Due  4/12/00 

A model of catalytic converter ignition consists of
the zeroth order kinetic model:

dT/dt = A * exp(-E/kT)

where E is the activation energy, k is Boltzman's
constant, and A is the preexponential rate
constant divided by the heat capacity.  Write an
adaptive algorithm using a local quadrature module
consisting of the G7-K15 quadrature rules to determine
the time necessary to go from a manifold temperature of
600K to the reaction temperature of 900K.  Use a 
tolerance of 1e-8.  Confirm your result by
comparing your algorithm to the matlab routine
'quad'.

Use the constants:
E/k = 9.1x10^3  K
A = 8.9x10^6 K/s

Hint:  obtain the time by integrating the inverse of
the reaction rate.

You will find the following weights and nodes for the
G7-K15 rules useful (based on the domain [-1,1]):

xs=[.949107912342758;.741531185599384;.405845151377397];
xs=[-xs;0;xs];
wxs=[.129484966168870,.279705391489277,.381830050505119];
wxs=[wxs,.417959183673469,wxs];
ys=[.991455371120813;.864864423359769;.586087235467691;...
    .207784955007898];
ys=[-ys;ys];
wxks=[.063092092629979,.140653259715525,.190350578064785];
wxks=[wxks,.209482141084728,wxks];
wyks=[.022935322010529,.104790010322250,.169004726639267,...
      .204432940075298];
wyks=[wyks,wyks];


Be sure to keep your solution to this problem (your adaptive
quadrature algorithm) in your Matlab toolbox - it's alot
better than the one that Matlab provides!