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In empirical risk optimization, it has been observed that stochastic gradient implementations that rely on random reshuffling of the data achieve better performance than implementations that rely on sampling the data uniformly. Recent works have purs
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fb30f3987ed0ad3f9ad752c53d999e2b
Autor:
Ali H. Bhrawy, Mohamed A. Abdelkawy
Publikováno v:
Journal of Computational Physics. 294:462-483
A shifted Legendre collocation method in two consecutive steps is developed and analyzed to numerically solve one- and two-dimensional time fractional Schrodinger equations (TFSEs) subject to initial-boundary and non-local conditions. The first step
Publikováno v:
Journal of Computational Physics. 293:142-156
In this paper, an efficient and accurate spectral numerical method is presented for solving second-, fourth-order fractional diffusion-wave equations and fractional wave equations with damping. The proposed method is based on Jacobi tau spectral proc
Publikováno v:
Numerical Algorithms. 71:151-180
The space-time fractional diffusion-wave equation (FDWE) is a generalization of classical diffusion and wave equations which is used in modeling practical phenomena of diffusion and wave in fluid flow, oil strata and others. This paper reports an acc
Autor:
Ali H. Bhrawy, Mahmoud A. Zaky
Publikováno v:
Journal of Computational Physics. 281:876-895
In this paper, we propose and analyze an efficient operational formulation of spectral tau method for multi-term time-space fractional differential equation with Dirichlet boundary conditions. The shifted Jacobi operational matrices of Riemann-Liouvi
Publikováno v:
Thermal Science, Vol 19, Iss suppl. 1, Pp 25-34 (2015)
In this paper, we are concerned with the fractional sub-diffusion equation with a non-linear source term. The Legendre spectral collocation method is introduced together with the operational matrix of fractional derivatives (described in the Caputo s
Autor:
Robert A. Van Gorder, Ali H. Bhrawy
Publikováno v:
Applied Mathematics & Information Sciences. 9:75-83
The Ito equation (a coupled nonlinear wave equation which generalizes the KdV equation) has previously been shown to admit a reduction to a single nonlinear Casimir equation governing the wave solutions. Some analytical properties of the solutions to
Autor:
Ali H. Kashmar, Eddie Shahril Ismail
Publikováno v:
Applied Mathematical Sciences. 9:4399-4412
Random Number Generators (RNGs) are applied in a wide variety of cryptographic operations such as cryptographic computer security protocols, encryption algorithms, and keystreams. Stream ciphers employ an encryption transformation which varies with t
Autor:
Mahmoud A. Zaky, Ali H. Bhrawy
Publikováno v:
Nonlinear Dynamics. 80:101-116
The cable equation plays a central role in many areas of electrophysiology and in modeling neuronal dynamics. This paper reports an accurate spectral collocation method for solving one- and two-dimensional variable-order fractional nonlinear cable eq
Publikováno v:
Nonlinear Analysis, Vol 19, Iss 4 (2014)
In this paper, a new spectral collocation method is applied to solve Lane–Emden equations on a semi-infinite domain. The method allows us to overcome difficulty in both the nonlinearity and the singularity inherent in such problems. This Jacobi rat