Nick Trefethen Comes to UW

by Nicholas Cain

Nick Trefethen is one of those speakers that you only have to hear once to become entirely hooked on his future lectures.  I have now attended three lectures in two days, and I have come away from each one with three entirely different and equally awesome ideas. Dr. Trefethen, currently of Oxford university and the President-elect of SIAM, gave a very exciting talk on last week showcasing the new developments of his matlab-based tool suite called chebfun.

In the earlier incarnations of chebfun that I have played around with in the past, one could approximate arbitrary functions with chebyshev polynomial interpolants.  Now it appears that the chebfun team (in large part due to Toby Driscoll and Asgeir Birkisson) has overloaded matlab’s “backslash” solver command to solve not only linear but nonlinear ODE BVP’s. For example, suppose you are interested in checking a solution from your perturbations homework, and want to solve .0001*u”(x) + x*u(x) = 0 for -1 < x <1, where u(-1) = 0 and u(1) = 1. Wouldn’t it be nice if matlab had a “one-liner” to show you how?

With the latest version of chebfuns, this is solved by:
>> [d,x,N] = domain(-1,1);
>> N.op = @(u) 0.0001*diff(u,2) + x.*u;
>> N.lbc = 0;
>> N.rbc = 1;
>> u = N; plot(u,’m’,LW,lw)

Painless and easy nonlinear BVP’s in matlab, who would have thought? Check out his page for more info; the software is incredibly simple to install and use.  If you know basic matlab, you can be underway in less than 5 minutes! And have fun!

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