Journal of Applied Mathematics and Computing最新文献

We introduce an innovative postprocessing technique aimed at refining the accuracy of the discontinuous Galerkin method for solving linear delay differential equations (DDEs) with vanishing delays. The fundamental idea behind this postprocessing technique is to enhance the discontinuous Galerkin solution of degree k by incorporating a generalized Jacobi polynomial of degree (k+1). We demonstrate that this postprocessing step enhances convergence by one order under the (L^infty )-norm. Moreover, we apply this technique to both nonlinear DDEs with vanishing delays and linear DDEs with non-vanishing delays. We further validated the theoretical results through a series of numerical examples.

In this paper, we establish a fast modified (overline{L1}) finite difference method for the time fractional diffusion equation with weakly singular solution at the initial moment. First, the time fractional derivative is approximated by the modified (overline{L1}) formula on graded meshes, and the spatial derivative is approximated by the standard central difference formula on uniform meshes. Therefore, a numerical scheme for the time fractional diffusion equation is obtained. Then, the Von-Neumann stability analysis method is used to analyze the stability of the scheme, and the truncation error estimate is given. On the other hand, the time fractional derivative is nonlocal, which has historical dependency, thus, the cost of computation and memory consumption are expensive. Based on the sum-of exponentials approximation (SOE) technique, we optimize the numerical format, reduce the complex amount from (O(Mhat{N})) to (O(M N_{exp})), and the amount of computation from (O(Mhat{N}^2)) to (O(Mhat{N}N_{exp})), where M, (hat{N}) and (N_{exp}) represent the number of spatial points, the number of temporal points, and the exponential amount, respectively. Finally, numerical examples verify the effectiveness of the scheme and theoretical analysis.

This study is devoted to the numerical investigation of linear and nonlinear hyperbolic telegraph equation. We have proposed a wavelet collocation method based on Legendre polynomials for approximating the solution. Both the spatial and temporal variables, along with their derivatives, are approximated using the Legendre wavelet and its integration. The present approach is simple, consistent and straightforward. To assure the theoretical consistency of the method, an estimate for the upper bound of the error norm is provided. We have proved an exponential order of convergence which is better than the methods available in the literature. Some numerical experiments are carried out to justify the theoretical results and the outcomes confirm the computational efficiency of the proposed method.

Fuzzy graphs find numerous applications in real life. One of the extensions of fuzzy graphs is Fermatean fuzzy graphs. Here, we introduce the concepts of Fermatean fuzzy set to the domain of graph theory and obtain a novel type of graph, referred to as Fermatean fuzzy graph ((textit{FFG})). The article establishes fundamental terms such as strong (textit{FFG}), complete (textit{FFG}), regular (textit{FFG}), path, degree, total degree, homomorphism, and isomorphism of (textit{FFG}), as well as the complement of (textit{FFG}). Alongside the introduction of these concepts, their important properties, theorems, and illustrative examples are defined and discussed. Finally, an application has surfaced suggesting the utilization of (textit{FFG})s to scrutinize the key factors affecting the productivity of Tata Motors, paving the way for a comprehensive analysis of the company’s operational efficiency using score function.

This paper examined the behavior of the HIV/AIDS epidemic stochastic model driven by both White Noise and Lévy jumps. Initially, we demonstrated that the stochastic model under consideration has one and only one positive solution which exists globally. Based on the analytical results on the model, we obtained the threshold parameters which are responsible for the eradication and the permanence of the disease. Finally, we verified our analytical results numerically.

This paper considers the problem of estimating reachable set in leaderless consensus for multi-agent systems with Lipschitz nonlinear dynamics and bounded external disturbances. Initially, a sampled-data control is introduced to address the consensus of nonlinear multi-agent systems vulnerable to deception attacks and packet dropouts, which occur randomly during sampling intervals. Then, aperiodic sampling in various degrees is taken into account in the primary Lyapunov term. Sufficient conditions to guarantee that all the actual states of the multi-agent, starting from the initial state, can be bounded within a given ellipsoid set are established by designing a suitable controller. Moreover, the consensus control design is established as linear matrix inequalities, utilizing a two-sided looped functional and Wirtinger’s inequality-based discontinuous Lyapunov–Krasovskii functional. Finally, the numerical section validates the applicability of the proposed control method.

In this paper, a SIS epidemic model with nonlinear incidence and ratio dependent pulse control is proposed and analyzed. Firstly, for the system that ignores the effect of pulses, the basic reproductive number (R_0) is derived using the next-generation matrix method, and the stability of the equilibria of the system is analyzed. And then the dynamics of the system containing pulse effects was investigated. The existence of periodic solutions has been proven by constructing appropriate Poincaré mappings and using the fixed point theorem. We found that pulses have a significant impact on system dynamics. Under the influence of pulses, the system trajectory undergoes periodic oscillations, which are verified by numerical simulations.

Nonlinear phenomena occur in diverse fields such as science, engineering and business. Research within computational science is continuously advancing, characterized by the development of new numerical techniques or the refinement of existing ones. However, these numerical techniques may be computationally expensive, while demonstrating superior convergence rate. By considering these demanding features, this paper aimed to devise new fourth- and eight-order iterative methods for root finding. This will be accomplished by taking the linear combination of Newton–Steffensen’s method and Yu and Xu’s method to obtain fourth-order method. We employed weight function approach to achieve eighth-order method. The proposed methods supports the Kung and Traub conjecture and hence are optimal by utilizing three function evaluations for fourth-order method and four functional evaluations for eighth-order method per cycle. The convergence criteria of the proposed schemes are thoroughly covered in the two primary theorems. To demonstrate the usefulness, validity and accuracy, we explore some real-world applications in civil and chemical engineering fields. In terms of the number of iterations, absolute residual errors, errors in consecutive iterations, the preassigned tolerance, convergence speed, percentage of convergent points, mean value of iterations for methods to converge and CPU time (sec), the numerical results obtained from the test examples illustrates that our proposed methods perform better than other methods of same order. Finally, several forms of complex functions are taken into consideration under basins of attraction in order to observe the overall fractal behavior of the proposed technique and some existing methods.

One of the global problems and a number of societal challenges in the areas of social life, the economy, and international communications is COVID-19. In order to counteract the impact of sickness on society, we created a deterministic COVID-19 model in this study that uses real data to assess the impact of disease, dynamical transmission, quarantine impact, and hospitalized treatment. The model includes a generalized form of the fractal and fractional operator. This study aims to develop a fractal-fractional mathematical model suitable for the lifestyle of the Thai population facing the COVID-19 situation. The model divides the incubation period into the quarantine class and the exposed class, which later moved to the hospitalized infected class and the infected class. The fractal-fractional derivative is used to analyze the dynamics of the population in these classes, providing a more detailed understanding of the epidemic’s progression and the effectiveness of control measures. The existence and uniqueness of the solution were also determined with the Lipschitz condition and fixed point theory. With the use of simulations and functional analysis tools like Ulam-Hyers, we examine the sensitivity analysis of the fractal-fractional model with respect to each parameter effect. We develop a numerical scheme for the fractal-fractional model based on Newton polynomial for computational analysis and convergence solution to steady-state points of real data COVID-19 in Thailand. The verification of the examined fractional-order model with actual COVID-19 data for Thailand demonstrates the potential of the suggested paradigm in forecasting and comprehending the dynamics of the pandemic. Furthermore, the fractal fractional-order derivative gives rise to a range of chaotic behaviors that show how the species has changed over place and time. Fractional-order epidemiological models may help predict and understand the course of the COVID-19 pandemic and provide relevant management approaches.

This paper considers the convergence analysis of the H-eigenvalues for a class of real symmetric and convergent tensor sequences. We first establish convergence results of some sequences of points. Then we study the behaviors of the H-eigenvalues and H-eigenvectors of the convergent tensor sequence. In particular, we obtain the convergence properties of the largest and smallest H-eigenvalues of the tensor sequence. Eventually, the corresponding numerical results are presented to verify our theoretical findings.