Search Results (5)

This paper introduces the exponential time differencing (ETD) technique as a numerical method to efficiently solve vulnerable American options pricing. We address several challenges, including removing cross-derivative terms through appropriate transformations, treating early-exercise opportunities using the penalty method, and substituting fixed boundary conditions with corresponding one-sided finite differences. The proposed method is shown to be both accurate and efficient through numerical experiments, which also compare the results with existing methods and analyze the numerical stability and convergence rate. Full article

A longitudinal study for 847 bladder cancer patients for a period of fifteen years is presented. After the first surgery, the patients undergo successive ones (recurrences). A state-model is selected for analyzing the evolution of the cancer, based on the distribution of the times between recurrences. These times do not follow exponential distributions, and are approximated by phase-type distributions. Under these conditions, a multidimensional Markov process governs the evolution of the disease. The survival probability and mean times in the different states (levels) of the disease are calculated empirically and also by applying the Markov model, the comparison of the results indicate that the model is well-fitted to the data to an acceptable significance level of 0.05. Two sub-cohorts are well-differenced: those reaching progression (the bladder is removed) and those that do not. These two cases are separately studied and performance measures calculated, and the comparison reveals details about the characteristics of the patients in these groups. Full article

This paper introduces the Fourier spectral method combined with the strongly stable exponential time difference method as an attractive and easy-to-implement alternative for the integration of the multi-dimensional Allen–Cahn equation with no-flux boundary conditions. The main advantages of the proposed method are that it utilizes the discrete fast Fourier transform, which ensures efficiency, allows an extension to two and three spatial dimensions in a similar fashion as one-dimensional problems, and deals with various boundary conditions. Several numerical experiments are carried out on multi-dimensional Allen–Cahn equations including a two-dimensional Allen–Cahn equation with a radially symmetric circular interface initial condition to demonstrate the fourth-order temporal accuracy and stability of the method. The numerical results show that the proposed method is fourth-order accurate in the time direction and is able to satisfy the discrete energy law. Full article

Enhancing the frequency band of the electromagnetic wave is regarded as an efficient way to solve the communication blackout problem. In this paper, frequency of incident wave is raised to Terahertz (THz) band and the radar cross section (RCS) of the three-dimensional conductive model is calculated and simulated based on the Runge–Kutta Exponential Time Differencing–Finite Difference Time Domain method (RKETD-FDTD). Interaction of THz wave and magnetized plasma sheath is discussed. Attenuations in incident wave frequencies of 0.34 THz and 3 GHz and different plasma densities are analyzed. The monostatic RCS is used to compare the penetration in different incident wave frequencies while the bistatic RCS is fixed on 0.34 THz to study its characteristics. The simulation result has almost the same RCS as that of the model without coating plasma when the frequency of incident wave reaches 0.34 THz. The advantages of THz wave at 0.34 THz on increasing RCS and reducing the attenuation are demonstrated from different aspects including polarizations, incident angles, magnetization and anisotropy of plasma, thickness of plasma, scan planes and inhomogeneous distribution of plasma. It can be concluded that 0.34 THz has unique advantages in increasing the radar cross section and can be applied to solve the problem of communication interruption. Full article

Wildfire regimes are changing across the globe with several ecosystems witnessing more frequent fires across longer fire seasons. The western United States is one such region. The NASA RECOVER Historic Fires Database (HFD) contains all documented wildfires across the western United States occurring between 1950 and 2019 (n = 55,566). This study analyzed the spatiotemporal patterns of these wildfires using ArcGIS Pro Geographic Information System (GIS) software to characterize changes in fire frequency, size, and severity over time. Analysis of annual fire frequency and acres burned reveals a near exponential growth in fire frequency (R² = 0.71, P < 0.001) and size (R² = 0.67, P < 0.001) since 1950. A comparison of mean and median acres burned annually suggests the occurrence of mega-fires (wildfires burning more than 100,000 acres) is also increasing. To illustrate this, this study found the mean size of fires occurring in the decade of the 1950s was 1204 acres while in the most recent decade (2010–2019) mean fire size has more than doubled, reaching an average of 3474 acres. The trend in fire severity between 2001 and 2017 used 365 Differenced Normalized Burn Ratio (dNBR) layers calculated using Landsat or Sentinel-2 satellite imagery. Results suggest fire severity has remained relatively stable in light of increasing fire frequency and size, however more research is required to more fully understand changes in fire severity. The results of this study and other related studies are important as they provide useful information to land managers and policy makers regarding the changing wildfire regime currently being witnessed across the western United States. Full article