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Fast Algorithms for Spectral Collocation with Non-Periodic Boundary Conditions
 

Summary: Fast Algorithms for Spectral Collocation with
Non-Periodic Boundary Conditions
W. Lyons a,1
, H. D. Ceniceros a,2
, S. Chandrasekaran b,1
and
M. Gu c
aDepartment of Mathematics, University of California, Santa Barbara, CA
93106-3080, USA
bDepartment of Electrical and Computer Engineering, University of California,
Santa Barbara, CA 93106-9560, USA
cDepartment of Mathematics, University of California, Berkeley, CA 94720-3840,
USA
Abstract
We present a method for the numerical solution of partial differential equations using
spectral collocation. By employing a structured representation of linear operators
we are able to use fast algorithms without being restricted to periodic boundary
conditions. The underlying ideas are introduced and developed in the context of
linearly implicit methods for stiff equations. We show how different boundary con-
ditions may be applied and illustrate the technique on the Allen-Cahn equation and

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics