Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High order algorithm for the time-tempered fractional Feynman-Kac
  equation   We provide and analyze the high order algorithms for the model describing the
functional distributions of particles performing anomalous motion with
power-law jump length and tempered power-law waiting time. The model is derived
in [Wu, Deng, and Barkai, Phys. Rev. E., 84 (2016), 032151], being called the
time-tempered fractional Feynman-Kac equation. The key step of designing the
algorithms is to discretize the time tempered fractional substantial
derivative, being defined as $${^S\!}D_t^{\gamma,\widetilde{\lambda}}
G(x,p,t)\!=\!D_t^{\gamma,\widetilde{\lambda}} G(x,p,t)\!-\!\lambda^\gamma
G(x,p,t) ~{\rm with}~\widetilde{\lambda}=\lambda+ pU(x),\, p=\rho+J\eta,\,
J=\sqrt{-1},$$ where $$D_t^{\gamma,\widetilde{\lambda}} G(x,p,t)
=\frac{1}{\Gamma(1-\gamma)} \left[\frac{\partial}{\partial
t}+\widetilde{\lambda} \right]
\int_{0}^t{\left(t-z\right)^{-\gamma}}e^{-\widetilde{\lambda}\cdot(t-z)}{G(x,p,z)}dz,$$
and $\lambda \ge 0$, $0<\gamma<1$, $\rho>0$, and $\eta$ is a real number. The
designed schemes are unconditionally stable and have the global truncation
error $\mathcal{O}(\tau^2+h^2)$, being theoretically proved and numerically
verified in {\em complex} space. Moreover, some simulations for the
distributions of the first passage time are performed, and the second order
convergence is also obtained for solving the `physical' equation (without
artificial source term).

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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph