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Solution of evolutionary PDEs using adaptive finite differences with
pseudospectral post-processing
D M Sloan , L S Mulholland & Y Qiu
Department of Mathematics,
University of Strathclyde,
Glasgow
Abstract
A coordinate transformation approach is described that enables pseudospectral
methods to be applied efficiently to unsteady differential problems with steep
solutions. The work is an extension of a method presented by Mulholland,
Huang and Sloan [1] for the adaptive pseudospectral solution of steady problems.
A coarse grid is generated by a moving mesh finite difference method that is
based on equidistribution, and this grid is used to construct a time-dependent
coordinate transformation. A sequence of spatial transformations may be
generated at discrete points in time, or a single transformation may be
generated as a continuous function of space and time. The differential problem
is transformed by the coordinate transformation and then solved by a method
that combines pseudospectral discretisation in space with a suitable integrator
in time. Numerical results are presented for unsteady problems in one space
dimension.
[1] L S Mulholland, W Z Huang & D M Sloan, Pseudospectral solution of near-singular
problems using numerical coordinate transformations based on adaptivity,
Strathclyde Maths. Research Report 13 (1995). Submitted for publication.
Last modified Fri Jun 21 19:19:16 GB-Eire 1996
(DBD)