Very-high-precision solutions of a class of Schr{ö}dinger equations

Details Very-high-precision solutions of a class of Schr{ö}dinger equations Very-high-precision solutions of a class of Schr{ö}dinger equations

2010-08-04

arxiv.org/abs/1008.0834v1

Computer Physics Communications 2011 ;Volume 182.(9) p. 1810-1813 NTNU

Physics

Mathematical Physics

4 page contribution to proceedings of the Conference on Computational Physics, June 23rd-26th 2010 in Trondheim (submitted to

Scientific paper

We investigate a method to solve a class of Schr{\"o}dinger equation eigenvalue problems numerically to very high precision $P$ (from thousands to a million of decimals). The memory requirement, and the number of high precision algebraic operations, of the method scale essentially linearly with $P$ when only eigenvalues are computed. However, since the algorithms for multiplying high precision numbers scale at a rate between $P^{1.6}$ and $P\,\log P\,\log\log P$, the time requirement of our method increases somewhat faster than $P^2$.

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