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

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 $P^2$.

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

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