In recent times, the derivation of Runge-Kutta methods based on averages other than the arithmetic mean is on the rise. In this paper, the authors propose a new version of explicit Runge-Kutta method, by introducing the harmonic mean as against the usual arithmetic averages in standard Runge-Kutta schemes.
In recent years, the derivation of Runge-Kutta methods with higher derivatives has been on the increase. In this paper, we present a new class of three stage Runge-Kutta method with first and second derivatives. The consistency and stability of the method is analyzed. Numerical examples with excellent results are shown to verify the accuracy of the proposed method compared with some existing methods.
The resurgence of the coronavirus (COVID-19) disease is rapidly taking its toll on many nations across the globe. As the situation rapidly evolves, the entire world is faced with difficult and challenging moment and the need to be safe from the disease. Several international efforts are geared towards the production of effective vaccine for curing the disease. But, pending the availability of such vaccine, the need to flatten the curves is now the top priority of both governmental and non-governmental organisations in Nigeria. Estimation of the basic reproduction number of the disease is crucial to understanding its dynamics and making suitable preventive policies that will slow the spread and ultimately flatten the curves. In this work, we propose a compartmental-based model for analysing the dynamics of the pandemics' second wave in Nigeria taking into consideration, the current control measures. Using the Quasi-Newton algorithm, the model is fitted to the available data provided by Nigeria Centre for Disease Control (NCDC), World Health Organization (WHO) and accessible on the Wolfram Data Repository. The basic reproduction number of the second wave of the disease in Nigeria is estimated using the model. The model was also used to estimate the infection rate, average latent time, average recovery rate and average mortality rate of the disease. Efficiency of the current control measures is also measured. Forecast of the turning points and possible vanishing time of the virus in Nigeria are made. The infection rate, average latent time, average recovery rate and average mortality rate of the disease are estimated. Also, the basic reproduction number of the disease in Nigeria is estimated. Predictions on the turning points and possible vanishing time of the virus in Nigeria are made. Recommendations on how to manage the resurgence of the disease in Nigeria are also suggested.
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