Computational and Mathematical Methods最新文献

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.

The Birnbaum–Saunders distribution is of particular interest for statistical inference. This distribution represents the failure time distribution in engineering. In addition, the Birnbaum–Saunders distribution is commonly used in different areas of science and engineering. Percentiles are a frequently employed statistical concept. Percentiles help ascertain the position of an observation concerning the percentage of data points below it. These percentiles serve as indicators of both the central tendency and the dispersion of data. While comparing two data distributions, the mean is typically the most dependable parameter for describing the population. However, in situations where the distribution exhibits significant skewness, percentiles may sometimes offer a more reliable representation. Herein, the confidence intervals for the difference between percentiles of Birnbaum–Saunders distributions were constructed by the generalized confidence interval (GCI) approach, the bootstrap approach, the Bayesian approach, and the highest posterior density (HPD) approach. A Monte Carlo simulation was conducted to evaluate the performance of the confidence intervals. The performance was considered via coverage probability and average width. The findings suggest that utilizing the GCI approach is advisable for estimating confidence intervals for the disparity between two percentiles. Ultimately, the outcomes of the simulation investigation, coupled with an application in the field of environmental sciences, were outlined.

In various fields, such as economics, finance, bioinformatics, geology, and medicine, namely, in the cases of electroencephalogram, electrocardiogram, and biotechnology, cluster analysis of time series is necessary. The first step in cluster applications is to establish a similarity/dissimilarity coefficient between time series. This article introduces an extension of the affinity coefficient for the autoregressive expansions of the invertible autoregressive moving average models to measure their similarity between them. An application of the affinity coefficient between time series was developed and implemented in R. Cluster analysis is performed with the corresponding distance for the estimated simulated autoregressive moving average of order one. The primary findings indicate that processes with similar forecast functions are grouped (in the same cluster) as expected concerning the affinity coefficient. It was also possible to conclude that this affinity coefficient is very sensitive to the behavior changes of the forecast functions: processes with small different forecast functions appear to be well separated in different clusters. Moreover, if the two processes have at least an infinite number of π- weights with a symmetric signal, the affinity value is also symmetric.

In this work, we suggest a new numerical scheme called the fractional higher order Taylor method (FHOTM) to solve fractional differential equations (FDEs). Using the generalized Taylor’s theorem is the fundamental concept of this approach. Then, the local truncation error generated by the suggested FHOTM is estimated by proving suitable theoretical results. At last, several numerical applications are given to demonstrate the applicability of the suggested approach in relation to their exact solutions.

This article proposes a collocation approach based on a redefined quintic B-spline basis for solving the time-fractional Whitham-Broer-Kaup equations. The presented method involves discretizing the time-fractional derivatives using an L₁-approximation scheme and then approximating the spatial derivatives using the redefined quintic B-spline basis. The von Neumann technique has been used to demonstrate that the proposed method is unconditionally stable. The error estimates are discussed and show that the proposed method is third-order convergent. The results demonstrate the potential of the proposed method as a reliable tool for solving fractional differential equations.