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arXiv · 1008.0834

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

Asif Mushtaq·Amna Noreen·Kåre Olaussen·Ingjald Øverbø
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Abstract

We investigate a method to solve a class of Schr{ö}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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Asif Mushtaq, Amna Noreen, Kåre Olaussen, Ingjald Øverbø. 2010-08-04. Very-high-precision solutions of a class of Schr{ö}dinger equations. https://doi.org/10.1016/j.cpc.2010.12.046

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