Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains
Date of Issue2013
School of Physical and Mathematical Sciences
This paper is concerned with approximation properties of orthonormal mapped Chebyshev functions (OMCFs) in unbounded domains. Unlike the usual mapped Chebyshev functions which are associated with weighted Sobolev spaces, the OMCFs are associated with the usual (non-weighted) Sobolev spaces. This leads to particularly simple stiffness and mass matrices for higher-dimensional problems. The approximation results for both the usual tensor product space and hyperbolic cross space are established, with the latter particularly suitable for higher-dimensional problems.
Journal of computational and applied mathematics
© 2013 Elsevier B.V. This is the author created version of a work that has been peer reviewed and accepted for publication by Journal of Computational and Applied Mathematics, Elsevier B.V. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [DOI: http://dx.doi.org/10.1016/j.cam.2013.09.024].