Boris Baeumer
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View article: A Higher Order Resolvent-positive Finite Difference Approximation for Fractional Derivatives
A Higher Order Resolvent-positive Finite Difference Approximation for Fractional Derivatives Open
We develop a finite difference approximation of order $α$ for the $α$-fractional derivative. The weights of the approximation scheme have the same rate-matrix type properties as the popular Grünwald scheme. In particular, approximate solut…
View article: Boundary conditions for nonlocal one-sided pseudo-differential operators and the associated stochastic processes II
Boundary conditions for nonlocal one-sided pseudo-differential operators and the associated stochastic processes II Open
We connect boundary conditions for one-sided pseudo-differential operators with the generators of modified one-sided Lévy processes. On one hand this allows modellers to use appropriate boundary conditions with confidence when restricting …
View article: Boundary conditions for nonlocal one-sided pseudo-differential operators and the associated stochastic processes I
Boundary conditions for nonlocal one-sided pseudo-differential operators and the associated stochastic processes I Open
We connect boundary conditions for one-sided pseudo-differential operators with the generators of modified one-sided Lévy processes. On one hand this allows modellers to use appropriate boundary conditions with confidence when restricting …
View article: Space‐time fractional Dirichlet problems
Space‐time fractional Dirichlet problems Open
This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time‐changed by an inverse stable subordinator whose index equals the order of…
View article: The self-thinning rule and plant population modelling with resource constraints
The self-thinning rule and plant population modelling with resource constraints Open
The Japan Agency for Marine-Earth Science and Technology contributed this challenge to the 2016 Mathematics-in-Industry New Zealand Study Group Workshop. It concerned implications of the self-thinning rule for modelling plant population ch…
View article: A Calibration Transform for Families of Spectroscopes
A Calibration Transform for Families of Spectroscopes Open
We seek a transform that will map between the outputs of pairs of similar spectroscopes. The spectroscopes are used to sort fruit and must regularly be calibrated to allow for seasonal fruit variation. The aim is to obtain transforms that …
View article: Boundary Conditions for Fractional Diffusion
Boundary Conditions for Fractional Diffusion Open
This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady…
View article: Fokker–Planck and Kolmogorov backward equations for continuous time random walk scaling limits
Fokker–Planck and Kolmogorov backward equations for continuous time random walk scaling limits Open
It is proved that the distributions of scaling limits of Continuous Time\nRandom Walks (CTRWs) solve integro-differential equations akin to Fokker-Planck\nEquations for diffusion processes. In contrast to previous such results, it is\nnot …