Numerical Solutions of the Mathematical Models on the Digestive System and COVID-19 Pandemic by Hermite Wavelet Technique

This article developed a functional integration matrix via the Hermite wavelets and proposed a novel technique called the Hermite wavelet collocation method (HWM). Here, we studied two models: the coupled system of an ordinary differential equation (ODE) is modeled on the digestive system by considering different parameters such as sleep factor, tension, food rate, death rate, and medicine. Here, we discussed how these parameters influence the digestive system and showed them through figures and tables. Another fractional model is used on the COVID-19 pandemic. This model is defined by a system of fractional-ODEs including five variables, called S (susceptible), E (exposed), I (infected), Q (quarantined), and R (recovered). The proposed wavelet technique investigates these two models. Here, we express the modeled equation in terms of the Hermite wavelets along with the collocation scheme. Then, using the properties of wavelets, we convert the modeled equation into a system of algebraic equations. We use the Newton–Raphson method to solve these nonlinear algebraic equations. The obtained results are compared with numerical solutions and the Runge–Kutta method (R–K method), which is expressed through tables and graphs. The HWM computational time (consumes less time) is better than that of the R–K method.

Tracing the Origin of Moving Groups. III. Detecting Moving Groups in LAMOST DR7

We revisit the moving groups (MGs) in the solar neighborhood with a sample of 91,969 nearby stars constructed from LAMOST DR7. Using the wavelet technique and Monte Carlo simulations, five MGs together with a new candidate located at V≃−130 km s−1 are detected simultaneously in V − U 2 + 2 V 2 space. Taking into account the other known MGs, we conclude that MGs in the Galactic disk are spaced by approximately 15–25 km s−1 along V velocity. The origin of detected MGs is analyzed through the distributions of [Fe/H]−[Mg/Fe] and ages. Our results support attributing the origin to the continuous resonant mechanisms probably induced by the bar or spiral arms of the Milky Way.

HYBRID NEURO-WAVELET MODEL FOR SHORT TERM LOAD FORECASTING

- Accuracy of the electricity load forecasting is crucial in providing better cost effective risk management plans. This paper proposes a Short Term Electricity Load Forecast (STLF) model with a high forecasting accuracy. A cascaded forward BPN neuro-wavelet forecast model is adopted to perform the STLF. The model is composed of several neural networks whose data are processed using a wavelet technique. The data to be used in the model is electricity load historical data. The historical electricity load data is decomposed into several wavelet coefficient using the Discrete wavelet transform (DWT). The wavelet coefficients are used to train the neural networks (NNs) and later, used as the inputs to the NNs for electricity load prediction. The Levenberg-Marquardt (LM) algorithm is selected as the training algorithm for the NNs. To obtain the final forecast, the outputs from the NNs are recombined using the same wavelet technique.

Haar wavelet technique applied on the functionally graded carbon nanotube reinforced conical shells to study free vibration and buckling behaviors in thermal environments

This article is provided to investigate the free vibrational behaviors accompanied by buckling characteristics of carbon nanotube-reinforced conical shells via the Haar wavelet technique. For a better performance in the thermal environments, materials used in the structure obey the temperature-dependent relations. On the other hand, carbon nanotubes are embedded across the thickness uniformly or functionally. Using Hamilton’s principle through the first-order shear deformation theory yields governing equations. Both dynamic and stability states are evaluated in the vicinity of equilibrium state and are also derived with regard to initial thermal stresses that are obtained via linear membrane technique in static analysis. The obtained partial differential equations are converted into ordinary ones with the aid of separating variable technique. Subsequently, the Haar wavelet approach is used to discretize the equations meridionally and transform them into new algebraic ones. Capability of this approach in calculation of frequencies with only a few numbers of the collocation points is demonstrated. Finally, to verify the integrity and precision of the proposed approach, some comparison studies are made with those of relevant results in the literature primarily. Thereafter, some effective parameters such as the geometry of nanotube, different boundary conditions, temperatures, and material properties are studied.