Faculty of Science and Engineering
http://hdl.handle.net/10034/305487
2021-10-25T11:18:28ZOscillatory and stability of a mixed type difference equation with variable coefficients
http://hdl.handle.net/10034/626004
Oscillatory and stability of a mixed type difference equation with variable coefficients
Yan, Yubin; Pinelas, Sandra; Ramdani, Nedjem; Yenicerioglu, Ali Fuat
The goal of this paper is to study the oscillatory and stability of the mixed type difference equation with variable coefficients \[
\Delta x(n)=\sum_{i=1}^{\ell}p_{i}(n)x(\tau_{i}(n))+\sum_{j=1}^{m}q_{j}(n)x(\sigma_{i}(n)),\quad n\ge n_{0}, \] where $\tau_{i}(n)$ is the delay term and $\sigma_{j}(n)$ is the advance term and they are positive real sequences for $i=1,\cdots,l$ and $j=1,\cdots,m$, respectively, and $p_{i}(n)$ and $q_{j}(n)$ are real functions. This paper generalise some known results and the examples illustrate the results.
2021-08-12T00:00:00ZSpatial discretization for stochastic semilinear subdiffusion driven by integrated multiplicative space-time white noise
http://hdl.handle.net/10034/626003
Spatial discretization for stochastic semilinear subdiffusion driven by integrated multiplicative space-time white noise
Yan, Yubin; Hoult, James; Wang, Junmei
Spatial discretization of the stochastic semilinear subdiffusion driven by integrated multiplicative space-time white noise is considered. The spatial discretization scheme discussed in Gy\"ongy \cite{gyo_space} and Anton et al. \cite{antcohque} for stochastic quasi-linear parabolic partial differential equations driven by multiplicative space-time noise is extended to the stochastic subdiffusion. The nonlinear terms $f$ and $\sigma$ satisfy the global Lipschitz conditions and the linear growth conditions. The space derivative and the integrated multiplicative space-time white noise are discretized by using finite difference methods. Based on the approximations of the Green functions which are expressed with the Mittag-Leffler functions, the optimal spatial convergence rates of the proposed numerical method are proved uniformly in space under the suitable smoothness assumptions of the initial values.
2021-08-12T00:00:00ZError estimates of a continuous Galerkin time stepping method for subdiffusion problem
http://hdl.handle.net/10034/626002
Error estimates of a continuous Galerkin time stepping method for subdiffusion problem
Yan, Yubin; Yan, Yuyuan; Liang, Zongqi; Egwu, Bernard
A continuous Galerkin time stepping method is introduced and analyzed for subdiffusion problem in an abstract setting. The approximate solution will be sought as a continuous piecewise linear function in time $t$ and the test space is based on the discontinuous piecewise constant functions. We prove that the proposed time stepping method has the convergence order $O(\tau^{1+ \alpha}), \, \alpha \in (0, 1)$ for general sectorial elliptic operators for nonsmooth data by using the Laplace transform method, where $\tau$ is the time step size. This convergence order is higher than the convergence orders of the popular convolution quadrature methods (e.g., Lubich's convolution methods) and L-type methods (e.g., L1 method), which have only $O(\tau)$ convergence for the nonsmooth data. Numerical examples are given to verify the robustness of the time discretization schemes with respect to data regularity.
The final publication is available at Springer via http://dx.doi.org/10.1007/s10915-021-01587-9.
CC Licence not permitted for AM version see https://www.springernature.com/gp/open-research/policies/journal-policies
2021-07-29T00:00:00ZMulti-metric Evaluation of the Effectiveness of Remote Learning in Mechanical and Industrial Engineering During the COVID-19 Pandemic: Indicators and Guidance for Future Preparedness
http://hdl.handle.net/10034/625615
Multi-metric Evaluation of the Effectiveness of Remote Learning in Mechanical and Industrial Engineering During the COVID-19 Pandemic: Indicators and Guidance for Future Preparedness
Behera, Amar Kumar; de Sousa, Ricardo Alves; Oleksik, Valentin; Dong, Jingyan; Fritzen, Daniel
This data set contains data collected from 5 universities in 5 countries about the effectiveness of e-learning during the COVID-19 pandemic, specifically tailored to mechanical and industrial engineering students. A survey was administered in May, 2020 at these universities simultaneously, using Google Forms. The survey had 41 questions, including 24 questions on a 5-point Likert scale. The survey questions gathered data on their program of study, year of study, university of enrolment and mode of accessing their online learning content. The Likert scale questions on the survey gathered data on the effectiveness of digital delivery tools, student preferences for remote learning and the success of the digital delivery tools during the pandemic. All students enrolled in modules taught by the authors of this study were encouraged to fill the survey up. Additionally, remaining students in the departments associated with the authors were also encouraged to fill up the form through emails sent on mailing lists. The survey was also advertised on external websites such as survey circle and facebook. Crucial insights have been obtained after analysing this data set that link the student demographic profile (gender, program of study, year of study, university) to their preferences for remote learning and effectiveness of digital delivery tools. This data set can be used for further comparative studies and was useful to get a snapshot of student preferences and e-learning effectiveness during the COVID-19 pandemic, which required the use of e-learning tools on a wider scale than previously and using new modes such as video conferencing that were set up within a short timeframe of a few days or weeks.
2021-07-27T00:00:00Z