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Fourth-order time-stepping for stiff PDEs on the sphere

Abstract:

We present in this paper algorithms for solving stiff PDEs on the unit sphere with spectral accuracy in space and fourth-order accuracy in time. These are based on a variant of the double Fourier sphere method in coefficient space with multiplication matrices that differ from the usual ones, and implicit-explicit time-stepping schemes. Operating in coefficient space with these new matrices allows one to use a sparse direct solver, avoids the coordinate singularity, and maintains smoothness at...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1137/17m1112728

Authors


More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Christ Church
Role:
Author
Publisher:
Society for Industrial and Applied Mathematics
Journal:
SIAM Journal on Scientific Computing More from this journal
Volume:
40
Issue:
1
Pages:
A421-A451
Publication date:
2018-02-15
Acceptance date:
2017-09-21
DOI:
EISSN:
1095-7197
ISSN:
1064-8275
Language:
English
Keywords:
Pubs id:
pubs:993761
UUID:
uuid:f89d8a06-3465-4705-913a-a230cd8f5313
Local pid:
pubs:993761
Source identifiers:
993761
Deposit date:
2019-04-23

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