Diagonalization of 1-D differential operators with piecewise constant coefficients using the uncertainty principle

Sarah D. Long, Somayyeh Sheikholeslami, James V. Lambers and Carley Walker

Mathematics and Computers in Simulation (MATCOM), 2019, vol. 156, issue C, 194-226

Abstract: A highly accurate and efficient numerical method is presented for computing the solution of a 1-D time-dependent partial differential equation in which the spatial differential operator features a piecewise constant coefficient defined on n pieces, in either self-adjoint and non-self-adjoint form, on a finite interval with periodic boundary conditions. The Uncertainty Principle is used to estimate the eigenvalues of the operator. Then, these estimates are used to construct a basis of eigenfunctions for use with a spectral method. The solution is presented as a truncated eigenfunction expansion, where each eigenfunction is a wave function that changes frequencies at the interfaces between different materials. Numerical experiments demonstrate the accuracy, efficiency and scalability of the method in comparison to other methods.

Keywords: Heat equation; Uncertainty principle; Interface problem; Spectral methods; Eigenfunction expansion (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475418302003
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:156:y:2019:i:c:p:194-226

DOI: 10.1016/j.matcom.2018.08.003

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().