Finite Domain Anomalous Spreading Consistent with First and Second Law

After reviewing the problematic behavior of some previously suggested finite interval spatial operators of the symmetric Riesz type, we create a wish list leading toward a new spatial operator suitable to use in the space-time fractional differential equation of anomalous diffusion when the transport of material is strictly restricted to a bounded domain. Based on recent studies of wall effects, we introduce a new definition of the spatial operator and illustrate its favorable characteristics. We provide two numerical methods to solve the modified space-time fractional differential equation and show particular results illustrating compliance to our established list of requirements, most important to the conservation principle and the second law of thermodynamics.Comment: 14 figure

Comparison of sequence accelerators forthe Gaver method of numerical Laplace transform inversion

AbstractThe sequence of Gaver functionals is useful in the numerical inversion of Laplace transforms. The convergence behavior of the sequence is logarithmic, therefore, an acceleration scheme is required. The accepted procedure utilizes Salzer summation, because in many cases the Gaver functionals have the asymptotic behavior ƒn(t) − ƒn(t) ∼ An−2 as n → ∞ for fixed t. It seems that no other acceleration schemes have been investigated in this area. Surely, the popular nonlinear methods should be more effective. However, to our surprise, only one nonlinear method was superior to Salzer summation, namely the Wynn rho algorithm

Numerical Inversion Methods for Computing Approximate p-Values

The paper considers the problem of computing p-values of non-standard distributions for which the characteristic function is available in closed form. When the characteristic function is a multivalued complex function, the standard numerical inversion method needs to be used with care as the integrand may become discontinous due to branch cuts. An alternative inversion method based on the Gaver-Wynn-Rho algorithm is shown to be a general and effective solution to the discontinuity problem as it works with real-valued functions. The method is illustrated with two well-known time series tests with non-standard distributions. Copyright Springer Science+Business Media, Inc. 2005characteristic function, numerical transform inversion, tail probability,