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 phi(hA) v, phi(z) = (e(z)-1)/z. In this way, it is possible to approximate.( 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 phi(k) functions, k >= 0.

Accurate evaluation of divided differences for polynomial interpolation of exponential propagators

CALIARI, Marco
2007

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 phi(hA) v, phi(z) = (e(z)-1)/z. In this way, it is possible to approximate.( 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 phi(k) functions, k >= 0.
accurate divided differences, Newton interpolation, exponential integrators
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/312197
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