Mathematics
http://hdl.handle.net/10034/623013
Thu, 06 Aug 2020 11:06:31 GMT2020-08-06T11:06:31ZSelf-Dual Codes using Bisymmetric Matrices and Group Rings
http://hdl.handle.net/10034/623560
Self-Dual Codes using Bisymmetric Matrices and Group Rings
Gildea, Joe; Kaya, Abidin; Korban, Adrian; Tylyshchak, Alexander
In this work, we describe a construction in which we combine together the idea of a
bisymmetric matrix and group rings. Applying this construction over the ring F4 + uF4 together
with the well known extension and neighbour methods, we construct new self-dual codes of length
68: In particular, we find 41 new codes of length 68 that were not known in the literature before.
http://hdl.handle.net/10034/623560New Extremal binary self-dual codes of length 68 from generalized neighbors
http://hdl.handle.net/10034/623555
New Extremal binary self-dual codes of length 68 from generalized neighbors
Gildea, Joe; Kaya, Abidin; Korban, Adrian; Yildiz, Bahattin
In this work, we use the concept of distance between self-dual codes, which generalizes the concept of a neighbor for self-dual codes. Using the $k$-neighbors, we are able to construct extremal binary self-dual codes of length 68 with new weight enumerators. We construct 143 extremal binary self-dual codes of length 68 with new weight enumerators including 42 codes with $\gamma=8$ in their $W_{68,2}$ and 40 with $\gamma=9$ in their $W_{68,2}$. These examples are the first in the literature for these $\gamma$ values. This completes the theoretical list of possible values for $\gamma$ in $W_{68,2}$.
http://hdl.handle.net/10034/623555Higher Order Time Stepping Methods for Subdiffusion Problems Based on Weighted and Shifted Grünwald–Letnikov Formulae with Nonsmooth Data
http://hdl.handle.net/10034/623491
Higher Order Time Stepping Methods for Subdiffusion Problems Based on Weighted and Shifted Grünwald–Letnikov Formulae with Nonsmooth Data
Yan, yubin; Wang, Yanyong; Yan, Yuyuan; Pani, Amiya K.
Two higher order time stepping methods for solving subdiffusion problems are studied in this paper.
The Caputo time fractional derivatives are approximated by using the weighted and shifted Gr\"unwald-Letnikov formulae
introduced in Tian et al. [Math. Comp. 84 (2015), pp. 2703-2727]. After correcting a few starting steps, the proposed time
stepping methods have the optimal convergence orders $O(k^2)$ and $ O(k^3)$, respectively for any fixed time $t$ for both smooth and nonsmooth data. The error estimates are proved by directly bounding the approximation errors of the kernel functions. Moreover, we also present briefly the applicabilities of
our time stepping schemes to various other fractional evolution equations. Finally,
some numerical examples are given to show that the numerical results are consistent with the proven theoretical results.
http://hdl.handle.net/10034/623491An analysis of the L1 scheme for stochastic subdiffusion problem driven by integrated space-time white noise
http://hdl.handle.net/10034/623490
An analysis of the L1 scheme for stochastic subdiffusion problem driven by integrated space-time white noise
Yan, Yubin; Yan, Yuyuan; Wu, Xiaolei
We consider the strong convergence of the numerical methods for solving stochastic subdiffusion problem driven by an integrated space-time white noise. The time fractional derivative is approximated by using the L1 scheme and the time fractional integral is approximated with the Lubich's first order convolution quadrature formula. We use the Euler method to approximate the noise in time and use the truncated series to approximate the noise in space. The spatial variable is discretized by using the linear finite element method. Applying the idea in Gunzburger \et (Math. Comp. 88(2019), pp. 1715-1741), we express the approximate solutions of the fully discrete scheme by the convolution of the piecewise constant function and the inverse Laplace transform of the resolvent related function. Based on such convolution expressions of the approximate solutions, we obtain the optimal convergence orders of the fully discrete scheme in spatial multi-dimensional cases by using the Laplace transform method and the corresponding resolvent estimates.
Tue, 02 Jun 2020 00:00:00 GMThttp://hdl.handle.net/10034/6234902020-06-02T00:00:00Z