Accurate evaluation of divided differences for polynomial interpolation of exponential propagators

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) = (ez −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 ϕk functions, k ≥ 0. AMS Subject Classifications: 65D05, 65D20, 65M20.

• Type: Journal
• Year: 2007
• Where: COMPUTING
• Authors: Marco Caliari
• Keywords: Accurate Divided Differences, COMPUTING 2007, Matrix Exponential Propagator, Order ϕk Functions