@Article{IJNAM-20-371,
author = {Vabishchevich , Petr N.},
title = {Exponent Splitting Schemes for Evolution Equations with Fractional Powers of Operators },
journal = {International Journal of Numerical Analysis and Modeling},
year = {2023},
volume = {20},
number = {3},
pages = {371--390},
abstract = {<p style="text-align: justify;">We have considered the Cauchy problem for a first-order evolutionary equation with
fractional powers of an operator. Such nonlocal mathematical models are used, for example, to
describe anomalous diffusion processes. We want the transition to a new level in time to be
solved usual problems. Computational algorithms are constructed based on some approximations
of operator functions. Currently, when solving stationary problems with fractional powers of an
operator, the most attention is paid to rational approximations. In the approximate solution
of nonstationary problems, we come to equations with an additive representation of the problem operator. Additive-operator schemes are constructed by using different variants of splitting
schemes. In the present work, the time approximations are based on approximations of the transition operator by the product of exponents. We use exponent splitting schemes of the first and
second-order accuracy. The results of numerical experiments for a two-dimensional model problem
with fractional powers of the elliptic operator are presented.</p>},
issn = {2617-8710},
doi = {https://doi.org/10.4208/ijnam2023-1015},
url = {http://global-sci.org/intro/article_detail/ijnam/21538.html}
}