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@article{Snowball:2021:imatrm/tnab001,
author = {Snowball, B and Olver, S},
doi = {imatrm/tnab001},
journal = {Transactions of Mathematics and Its Applications},
pages = {1--37},
title = {Sparse spectral methods for partial differential equations on spherical caps},
url = {http://dx.doi.org/10.1093/imatrm/tnab001},
volume = {5},
year = {2021}
}

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TY  - JOUR
AB  - In  recent  years,  sparse  spectral  methods  for  solving  partial  differential  equationshave  been  derived  using  hierarchies  of  classical  orthogonal  polynomials  on  intervals,disks, disk-slices and triangles.  In this work we extend the methodology to a hierarchyof non-classical multivariate orthogonal polynomials on spherical caps.  The entries ofdiscretisations of partial differential operators can be effectively computed using for-mulae in terms of (non-classical) univariate orthogonal polynomials.  We demonstratethe results on partial differential equations involving the spherical Laplacian and bihar-monic operators, showing spectral convergence with discretisations that can be madewell-conditioned using a simple preconditioner.
AU  - Snowball,B
AU  - Olver,S
DO  - imatrm/tnab001
EP  - 37
PY  - 2021///
SN  - 2398-4945
SP  - 1
TI  - Sparse spectral methods for partial differential equations on spherical caps
T2  - Transactions of Mathematics and Its Applications
UR  - http://dx.doi.org/10.1093/imatrm/tnab001
UR  - https://academic.oup.com/imatrm/article/5/1/tnab001/6432392
UR  - http://hdl.handle.net/10044/1/92313
VL  - 5
ER  -

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