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Numerical treatment of the generalized time-fractional Huxley-Burgers’ equation and its stability examination

Hadhoud Adel R., Alaal Faisal E. Abd, Abdelaziz Ayman A., Radwan Taha

Demonstratio Mathematica

2021

Vol. 54, nr 1

436--451

In this paper, we show how to approximate the solution to the generalized time-fractional Huxley-Burgers’ equation by a numerical method based on the cubic B-spline collocation method and the mean value theorem for integrals. We use the mean value theorem for integrals to replace the time-fractional derivative with a suitable approximation. The approximate solution is constructed by the cubic B-spline. The stability of the proposed method is discussed by applying the von Neumann technique. The proposed method is shown to be conditionally stable. Several numerical examples are introduced to show the efficiency and accuracy of the method.

A statistical study of COVID-19 pandemic in Egypt

Radwan Taha

Demonstratio Mathematica

2021

Vol. 54, nr 1

233--244

The spread of the COVID-19 started in Wuhan on December 31, 2019, and a powerful outbreak of the disease occurred there. According to the latest data, more than 165 million cases of COVID-19 infection have been detected in the world (last update May 19, 2021). In this paper, we propose a statistical study of COVID-19 pandemic in Egypt. This study will help us to understand and study the evolution of this pandemic. Moreover, documenting of accurate data and taken policies in Egypt can help other countries to deal with this epidemic, and it will also be useful in the event that other similar viruses emerge in the future. We will apply a widely used model in order to predict the number of COVID-19 cases in the coming period, which is the autoregressive integrated moving average (ARIMA)model. This model depicts the present behaviour of variables through linear relationship with their past values. The expected results will enable us to provide appropriate advice to decision-makers in Egypt on how to deal with this epidemic.