Note on a differentiation formula, with application to the two-dimensional Schrödinger equation

Alexander Pikovski

PLOS ONE, 2017, vol. 12, issue 2, 1-6

Abstract: A method for obtaining discretization formulas for the derivatives of a function is presented, which relies on a generalization of divided differences. These modified divided differences essentially correspond to a change of the dependent variable. This method is applied to the numerical solution of the eigenvalue problem for the two-dimensional Schrödinger equation, where standard methods converge very slowly while the approach proposed here gives accurate results. The presented approach has the merit of being conceptually simple and might prove useful in other instances.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0171444

DOI: 10.1371/journal.pone.0171444

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