No abstract

The spread of the COVID-19 disease has had significant social and economic impacts all over the world. Numerous measures such as school closures, social distancing, and travel restrictions were implemented during the COVID-19 pandemic outbreak. Currently, as we move into the post-COVID-19 world, we must be prepared for another pandemic outbreak in the future. Having experienced the COVID-19 pandemic, it is imperative to ascertain the conclusion of the pandemic to return to normalcy and plan for the future. One of the beneficial features for deciding the termination of the pandemic disease is the small value of the case fatality rate (CFR) of coronavirus disease 2019 (COVID-19). There is a tendency of gradually decreasing CFR after several increases in CFR during the COVID-19 pandemic outbreak. However, it is difficult to capture the time-dependent CFR of a pandemic outbreak using a single exponential coefficient because it contains multiple exponential decays, i.e., fast and slow decays. Therefore, in this study, we develop a mathematical model for estimating and predicting the multiply exponentially decaying CFRs of the COVID-19 pandemic in different nations: the Republic of Korea, the USA, Japan, and the UK. We perform numerical experiments to validate the proposed method with COVID-19 data from the above-mentioned four nations.

In this study, we present benchmark problems for the numerical methods of the phase-field equations. To find appropriate benchmark problems, we first perform a linear stability analysis and then take a growth mode solution as the benchmark problem, which is closely related to the dynamics of the original governing equations. As concrete examples, we perform convergence tests of the numerical methods of the Allen–Cahn (AC) and Cahn–Hilliard (CH) equations using the proposed benchmark problems. The one- and two-dimensional computational experiments confirm the accuracy and efficiency of the proposed scheme as the benchmark problems.

In this study, we propose an unconditionally stable temporally second-order accurate scheme for a parabolic sine-Gordon equation. The proposed scheme is based on an operator splitting method. We solve linear and nonlinear equations using a Fourier spectral method and a closed-form solution, respectively. The proposed numerical method is temporally second-order accurate and unconditionally stable. To verify the superior efficiency and accuracy of the proposed scheme, we conduct various numerical tests. Computational tests validate the accuracy, efficiency, and simplicity of the proposed scheme.

<abstract><p>In this paper, we propose a novel, simple, efficient, and explicit numerical method for the Allen–Cahn (AC) equation on effective symmetric triangular meshes. First, we compute the net vector of all vectors starting from each node point to its one-ring neighbor vertices and virtually adjust the neighbor vertices so that the net vector is zero. Then, we define the values at the virtually adjusted nodes using linear and quadratic interpolations. Finally, we define a discrete Laplace operator on triangular meshes. We perform several computational experiments to demonstrate the performance of the proposed numerical method for the Laplace operator, the diffusion equation, and the AC equation on triangular meshes.</p></abstract>