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Accurate evaluation of divided differences for polynomial interpolation of exponential propagators

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Abstract

In this paper, we propose an approach to the computation of more accurate divided differences for the interpolation in the Newton form of the matrix exponential propagator φ(hA)v, φ (z) = (e z − 1)/z. In this way, it is possible to approximate φ (hA)v with larger time step size h than with traditionally computed divided differences, as confirmed by numerical examples. The technique can be also extended to “higher” order φ k functions, k≥0.

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  1. Department of Pure and Applied Mathematics, University of Padova, Via Trieste 63, 35121, Padova, Italy

    M. Caliari

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  1. M. Caliari
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Caliari, M. Accurate evaluation of divided differences for polynomial interpolation of exponential propagators. Computing 80, 189–201 (2007). https://doi.org/10.1007/s00607-007-0227-1

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