Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-04-26
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
29 pages, 11 figures, uses psfrag and hyperref, large parts rewritten in order to match to the requirements of the journal, co
Scientific paper
10.1016/j.jcp.2009.05.037
We introduce a single patch collocation method in order to compute solutions of initial value problems of partial differential equations whose spatial domains are 3-spheres. Besides the main ideas, we discuss issues related to our implementation and analyze numerical test applications. Our main interest lies in cosmological solutions of Einstein's field equations. Motivated by this, we also elaborate on problems of our approach for general tensorial evolution equations when certain symmetries are assumed. We restrict to U(1)- and Gowdy symmetry here.
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