A fast algorithm for the approximate solution of the discrete Wiener-Hopf equation is described and convergence rate estimates are obtained. The numerical algorithm is constructed by using the discrete Fourier transformation.

In the framework of Kramers’ rate theory, numerical determination of the distribution of energies is considered for protons transferred in perovskite-like oxides. By referring to the calculational procedures developed in the preceding paper (Samgin and Ezin, Ionics 14: 345–348, 2008), we find that, in many cases, depending upon the value of the energy loss parameter, the distribution in the barrier region is essentially other than the traditional Boltzmann’s distribution. The numerically simulated distributions are briefly analyzed to highlight the collectiveness of the proton transfer mechanism.

On a fast algorithm for the approximate solution of the discrete Wiener-Hopf equation and an estimation of the accuracy

Citations

Simulation of prefactor anomalies in superionic conductors in the case of arbitrary energy losses. II. Energy distributions in the barrier region

References

Some classes of singular equations

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