Paper Info
Title
A class of upwind methods based on generalized eigenvectors for weakly hyperbolic systems
Abstract
In this article, a class of upwind schemes is proposed for systems, each of which yields an incomplete set of linearly independent eigenvectors. The theory of Jordan canonical forms is used to complete such sets through the addition of generalized eigenvectors. A modified Burgers’ system and its extensions generate δ,δ′, δ″,⋯,δn waves as solutions. The performance of flux difference splitting-based numerical schemes is examined by considering various numerical examples. Since the flux Jacobian matrix of pressureless gas dynamics system also produces an incomplete set of linearly independent eigenvectors, a similar framework is adopted to construct a numerical algorithm for a pressureless gas dynamics system.
Year
DOI
Venue
2020
10.1007/s11075-019-00717-7
Numerical Algorithms
Keywords
Field
DocType
Weakly hyperbolic systems, Jordan canonical forms, Generalized eigenvectors, Upwind schemes, 15A21, 35L40, 35L65, 65M08
Linear independence,Jacobian matrix and determinant,Mathematical analysis,Generalized eigenvector,Hyperbolic systems,Canonical form,Flux,Upwind scheme,Eigenvalues and eigenvectors,Mathematics
Journal
Volume
Issue
ISSN
83
3
1572-9265
Citations 
PageRank 
References 
0
0.34
0
Authors
1
Name
Order
Citations
PageRank
Naveen Kumar Garg100.34