Exponential Time Differencing Method for Studying Prey-Predator Dynamic during Mating Period

This paper addresses a first numerical simulation to the nonlinear dynamic system of equations that describes the prey-predator model at the predator mating period. Some male species accompany the females during the mating period. In this case, both male and female feed on the same prey. The presented work shows the numerical solution for this specific case of the prey-predator mathematical model via an exponential time differencing method. In addition, the paper provides the biological implication of the solution.

Memory-Dependent Model for the Dynamics of COVID-19 Pandemic

COVID-19 pandemic has impacted people all across the world. As a result, there has been a collective effort to monitor, predict, and control the spread of this disease. Among this effort is the development of mathematical models that could capture accurately the available data and simulate closely the futuristic scenarios. In this paper, a fractional-order memory-dependent model for simulating the spread of COVID-19 is proposed. In this model, the impact of governmental action and public perception are incorporated as part of the time-varying transmission rate. The model simulation is performed using the two-step generalized exponential time-differencing method and tested for data from Wuhan, China. The mean-square errors demonstrate the merit of the fractional-order model and provide a good estimate of the optimal order.

Introducing Undergraduate Students to Nonlinear Dynamics through A Numerical Approach

This paper describes a numerical method that used to solve the nonlinear Schr\"{o}dinger equation. The methods are an exponential time differencing method and a spectral method. The result indicates that at a certain parameter, fluctuation of wave function has contained chaotic dynamics. This case is expected to be used as an example for introducing numerical methods to undergraduate students on nonlinear dynamics. This introduction is deemed necessary, referring to the curriculum and syllabus used in several educational institutions in various countries that have included the topic of nonlinearity.