Computational and Mathematical Methods最新文献

Market fluctuations in the stock sector are common. The possible loss that investors may incur because of their investment activity is referred to as investment risk. Returns on investments may fall short of expectations due to a variety of circumstances. Fit of the model to the data; performance in representing volatility, prediction, stability, and analysis; and interpretation goals are all factors to consider. This study investigates the volatility of the Indonesian composite index (ICI) using the GARCH-MIDAS model, integrating daily ICI returns with monthly macroeconomic indicators: Indonesian bank interest rates (BIIR), consumer price index (CPI), effective federal fund rate (EFFR), and inflation rate (IR). We begin by graphically analysing the trends in ICI returns and macroeconomic variables to identify potential patterns and shifts. Descriptive statistics offer a detailed numerical summary, setting the stage for in-depth empirical analysis. The long-run component of stock market volatility is estimated using the GARCH-MIDAS model, with macroeconomic variables included to capture their impact on market fluctuations. Maximum likelihood estimation (MLE) is employed to estimate the model parameters, ensuring a robust fit to the observed data. Our findings indicate that the EFFR has the most significant impact on ICI volatility, contrary to previous studies. Forecasting performance is evaluated using mean squared error (MSE) and mean absolute error (MAE), confirming the superior predictive capability of the EFFR variable. The study assesses risk using value at risk (VaR) for the ICI, incorporating the EFFR to account for macroeconomic influences on market volatility. VaR values at 99% and 95% confidence levels provide insights into potential maximum losses, aiding in informed investment decision-making. This research enhances knowledge of the relationship between macroeconomic variables and stock market volatility, providing investors and policymakers with important information for risk management and investment strategy optimization in the Indonesian equity market.

In this study, the Bernoulli subequation method (BS-EM) is applied to investigate the traveling wave solutions of the (2 + 1)-dimensional resonant Davey–Stewartson system. By employing a wave transformation, the system’s nonlinear partial differential equation is reduced to a nonlinear ordinary differential equation, which is then solved using the BS-EM approach. As a result, several new traveling wave solutions, which have not been previously reported in the literature, have been successfully obtained. These solutions provide new insights into the physical dynamics of the system and also satisfy the (2 + 1)-dimensional time–fractional resonant Davey–Stewartson equation. Furthermore, the analytical and graphical analyses of the obtained solutions have been carried out, and the wave profiles have been examined under various parameter conditions. All computations and graphical visualizations in this study were performed using the Wolfram Mathematica 12 software.

This paper is aimed at studying the dynamics of community transmission of HIV by constructing a fractal fractional mathematical model whose kernel is a generalized Mittag–Leffler type. First, we collect and analyze statistical data for epidemiological surveillance of HIV/AIDS prevalence in Yemen from 2000 to 2022. Then, we employ the statistical analysis software EViews and apply ARIMA models to predict the number of HIV/AIDS cases from 2023 to 2024. The results of the selected model, free of standard problems, predicted a future increase in HIV/AIDS cases in Yemen. Next, relying on the well-known fixed-point theorem and a set of other associated results, we prove the existence and uniqueness results of the fractional model. Moreover, we use the Adams–Bashforth method to approximate the solutions of this system numerically. Finally, we plot, tabulate, and simulate our results using the Mathematica software and compare them to the results obtained from the statistical model.

In the topic of discrete variable-order systems governed by fractional difference equations, this study makes a significant contribution by introducing two innovative variable-order versions of the fractional Grassi–Miller system. These new formulations are aimed at deepening our understanding of the complex dynamics that such systems exhibit. The research specifically delves into the chaotic dynamical behaviors manifested by these systems: one version being the fractional Grassi–Miller map with commensurate variable order and the other being the fractional Grassi–Miller map with incommensurate variable order. To provide a comprehensive analysis, this study incorporates a variety of variable orders, encompassing both exponential and sinusoidal functions. These variable orders are crucial in exploring how different functional forms influence the behavior of the system. By varying these orders, the research seeks to uncover the patterns and chaotic dynamics that emerge under different conditions. A suite of advanced numerical methods is employed to rigorously analyze and validate the presence of chaotic attractors in these newly proposed variable fractional versions of the Grassi–Miller system. The methods used include bifurcation diagrams, phase portraits, Lyapunov exponents, approximate entropy, C₀ complexity, and 0–1 test for chaos. Through the application of these numerical methods, the study thoroughly validates the existence of chaotic attractors in the proposed variable fractional versions of the Grassi–Miller system. The findings underscore the rich and complex behaviors that arise from different variable orders, offering new insights into the dynamics of fractional-order systems.

In today’s data-driven decision-making era, acquiring accurate information is vital. However, survey research faces challenges with sensitive issues. To address this, the Composite Randomized Response Technique (CRRT) was introduced in estimating the proportion of respondents possessing sensitive attributes. This study revealed that as the model captures more and more people involved in the sensitive attributes (π_s) from 0.1 to 0.4, the relative efficiency of CRRT increases from 2.2217 to 678.7843. Hence, CRRT was found to be more efficient than the conventional model, making it a robust approach for surveys targeting sensitive attributes, enhancing data accuracy, and supporting effective policy evaluation and resource allocation.

In this study, we discuss the approximate solution of the Harry Dym nonlinear partial differential equation and its integrodifferential version. We first construct the Picard successive approximation for the equations under consideration. Then, we give a detailed calculation of the approximate solution for two cases of the partial Harry Dym integrodifferential equation. The approximate solutions are illustrated for some chosen values of the arbitrary constants. The efficiency of this semianalytical method is demonstrated through discussing the regions of the domain with small errors as well as by extracting the exact solution from the limit of the approximation.

This study delves into the often-overlooked impact of immature mosquitoes on the dynamics of malaria transmission. By employing a mathematical model, we explore how these aquatic stages of the vector shape the spread of the disease. Our analytical findings are corroborated through numerical simulations conducted using the Runge–Kutta fourth-order method in MATLAB. Our research highlights a critical factor in malaria epidemiology: the basic reproduction number $$. We demonstrate that when $$ is below unity $$, the disease-free equilibrium exhibits local asymptotic stability. Conversely, when $$ surpasses unity $$, the disease-free equilibrium becomes unstable, potentially resulting in sustained malaria transmission. Furthermore, our analysis covers equilibrium points, stability assessments, bifurcation phenomena, and sensitivity analyses. These insights shed light on essential aspects of malaria control strategies, offering valuable guidance for effective intervention measures.

In this study, we consider a parameter-uniform convergent numerical approach for a class of time-fractional singularly perturbed partial differential equations (TF-SPDPDEs) with large delay in time that exhibits a regular exponential boundary layer on the right side of the spatial domain. An arbitrary very small parameter ε(0 < ε < <1) multiplies the highest-order derivative term of these singularly perturbed problems. The time-fractional derivative is considered in the Caputo sense with order α ∈ (0, 1). The numerical scheme comprises the L1 scheme and nonstandard finite difference method (FDM) for discretizing the time and space variables, respectively, on a uniform mesh. To show the parameter uniform convergence of the proposed method, the truncation error and stability analysis are discussed. The method is shown to be parameter-uniform convergent of order O((Δt)^2−α + Δx), where Δt and Δx are the step sizes in the time and space directions, respectively. In order to confirm the theoretical predictions, two numerical examples are presented, and the numerical results support the theoretical concepts discussed. Finally, to show the advantage of the proposed scheme, we made comparisons with the existing numerical methods in the literature, and the numerical results reveal that the present scheme is more accurate.

Predicting mortality in COVID-19 is one of the most significant and difficult tasks at hand. This study compares time series and machine learning methods, including support vector machines (SVMs) and neural networks (NNs), to forecast the mortality rate in seven countries: the United States, India, Brazil, Russia, France, China, and Bangladesh. Data were gathered between December 31, 2019, when COVID-19 began, and March 31, 2021. The study used 457 observations with 4 variables: daily confirmed cases, daily deaths, daily mortality rate, and date. To predict the death rate in the seven countries that were chosen, the data were analyzed using time series analysis and machine learning techniques. Models were compared to obtain more accurate mortality predictions. The autoregressive integrated moving average (ARIMA) model with the lowest AIC value for each nation is found through time series analysis. By increasing the hidden layer and applying machine learning techniques, the NN model for each country is chosen, and the optimal model is determined by determining the model with the lowest error value. Additionally, SVM analyzes every country and calculates its R² and root-mean-square error (RMSE). The lowest RMSE value is used to compare all of the time series and machine learning models. According to the comparison table, SVM provides a more accurate model to predict the mortality rate of the seven countries, with the lowest RMSE value. During the study period, mortality rates increased in Brazil and Russia and decreased in the United States, India, France, China, and Bangladesh, according to the comparison value of RMSE in this study. Furthermore, this paper shows that SVM outperforms all other models in terms of performance. According to the author’s analysis of the data, SVM is a machine learning technique that can be used to accurately predict mortality in a pandemic scenario.

Grey systems theory can be used to predict the evolution of a system with insufficient information. Unfortunately, the most used version of the grey model (GM), namely, GM(1,1), works best when the system series have an increasing exponential rate. In any other case, the GM(1,1) produces inaccurate predictions. In this paper, we examine the mathematical formulation of the conventional GM(1,1) in order to propose a new GM that addresses its shortcomings through a new time response function. Examples are presented to demonstrate the flexibility and accuracy of the new model when implemented with series of various natures. Comparisons with other intelligent GM(1,1) show that the proposed model performs better than the reference models.