SINC-PACK, A Family of Programs for Computation
Author:
Frank Stenger, School of Computing
Abstract:
This talk is about SINC-PACK - a family of computer programs for
carrying out a variety computations, for science and engineering. The
package is written in Matlab, and can be run with Matlab. The
programs of the package are especially effective for problems with
singularities, for problems over infinite regions, and for PDE
problems.
For example, in one dimension, the program enables does the following,
over finite, semi-infinite, infinite intervals or contours:
interpolation, differentiation, definite and indefinite integration,
definite and indefinite convolution, Hilbert and Cauchy transforms,
inversion of Laplace transforms and solution of ordinary differential
equation initial value problems.
In more than one dimension, the program solves linear and nonlinear
elliptic, hyperbolic, and parabolic partial differential equations, as
well as integral equations and conformal map problems. The regions
for these problems can be curvilinear (yet we still get separation of
variables, enabling solution via a finite sequence of one-dimensional
methods) finite, or infinite. The rate of convergence of the programs
of SINC-PACK is usually orders of magnitude faster than that of
current (e.g., finite element, finite difference methods, or
spectral methods).
A number of examples of solutions to problems are illustrated, to
provide a flavor of the power of the package.