Mathematics and Computers in Simulation最新文献

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Exploring computationally efficient stable numerical techniques for fractional Keller–Segel system modeling chemotaxis

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2024-12-21 DOI: 10.1016/j.matcom.2024.12.011

B Sagar , S. Saha Ray

Chemotaxis is a biological phenomenon whereby unicellular organisms direct their movements in response to certain chemicals in their habitat. This study presents a numerical investigation of the fractional Keller–Segel model describing the aggregation of cellular slime molds and bacterial chemotaxis. Two numerical schemes are provided to solve this model; primarily, a meshfree numerical scheme based on the local radial basis function partition of unity method is presented. In this approach, the domain is split up into a number of smaller, overlapping subdomains, and the radial basis function interpolation is performed separately on each of these. On the other hand, a numerical method employing the L1 scheme for temporal discretization and centered difference for spatial discretization is introduced to compare the primary proposed method solutions with the simulations acquired by this method. Stability and convergence of the time-discrete algorithm are rigorously established. The strengths of the carried work is that the proposed approach is meshfree, where as the classical methods like finite difference/element approaches depends on mesh. Also, as per the best of authors knowledge, the analytical solutions of the considered fractional model are not known in literature, which makes the carried numerical investigation innovative. Computational experiments are carried out, and simulation results of both schemes are compared. Also, the density plots of cellular slime mold and the chemical attractant for specific biological parameters are illustrated to observe their biological behavior.

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引用次数: 0

Markovian queueing model under Bernoulli vacation and servers’ malfunctioning: Metaheuristic optimization technique

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2024-12-20 DOI: 10.1016/j.matcom.2024.12.016

Sonali Thakur , Anamika Jain

Bernoulli vacation and effect of malfunctioning are analyzed for Markovian queueing single server model. Server is allowed to opt for the vacation with probability or can serve the upcoming failed unit with probability under the Bernoulli vacation. Meanwhile during busy state servers can face malfunctioning and to overcome this situation a quick repair is imposed to sustain the server in the working state. Performance measures are estimated by framing the Chapman-Kolmogorov equation and the further impact of the model on average expected queue length of units, servers’ reliability and servers’ availability factors are analyzed through R-K fourth order method. Moreover, the cost function is formulated, and the direct search method is used to study the cost variation for the designed model. To explore the economic benefits of the model, the minimum cost is optimized by the meta-heuristic soft computing optimization techniques SCA, TLBO, PSO and GSA. A comparative analysis examines the best approach among the described optimization techniques. Different techniques are used to get the best results and better allocation of resources to achieve efficient costs.

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引用次数: 0

Effective polygonal mesh generation and refinement for VEM

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2024-12-20 DOI: 10.1016/j.matcom.2024.12.007

Stefano Berrone , Fabio Vicini

In the present work we introduce a novel refinement algorithm for two-dimensional elliptic partial differential equations discretized with Virtual Element Method (VEM). The algorithm improves the numerical solution accuracy and the mesh quality through a controlled refinement strategy applied to the generic polygonal elements of the domain tessellation. The numerical results show that the outlined strategy proves to be versatile and possibly applicable to each two-dimensional problem where polygonal meshes offer advantages. In particular, we focus on the simulation of flow in fractured media, specifically using the Discrete Fracture Network (DFN) model. A residual a-posteriori error estimator tailored for the DFN case is employed. We chose this particular application to emphasize the effectiveness of the algorithm in handling complex geometries. All the numerical tests demonstrate optimal convergence rates for all the tested VEM orders.

引用次数: 0

Decomposition of the option pricing formula for infinite activity jump-diffusion stochastic volatility models

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2024-12-18 DOI: 10.1016/j.matcom.2024.12.010

Youssef El-Khatib , Zororo S. Makumbe , Josep Vives

Let the log returns of an asset

X_{t} = log (S_{t})

be defined on a risk neutral filtered probability space

(Ω, F, {(F_{t})}_{t \in [0, T]}, P)

for some

0 < T < \infty

. Assume that

X_{t}

is a stochastic volatility jump-diffusion model with infinite activity jumps. In this paper, we obtain an Alós-type decomposition of the plain vanilla option price under a jump-diffusion model with stochastic volatility and infinite activity jumps via two approaches. Firstly, we obtain a closed-form approximate option price formula. The obtained formula is compared with some previous results available in the literature. In the infinite activity but finite variation case jumps of absolute size smaller than a given threshold

ɛ

are approximated by their mean while larger jumps are modeled by a suitable compound Poisson process. A general decomposition is derived as well as a corresponding approximate version. Lastly, numerical approximations of option prices for some examples of Tempered Stable jump processes are obtained. In particular, for the Variance Gamma one, where the approximate price performs well at the money.

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引用次数: 0

An EKF prediction of COVID-19 propagation under vaccinations and viral variants

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2024-12-17 DOI: 10.1016/j.matcom.2024.12.012

Xinhe Zhu, Yuanyou Shi, Yongmin Zhong

The COVID-19 pandemic continues to pose significant challenges to global public health, requiring advanced predictive mathematical models for prediction, prevention and control. This paper proposes a novel approach to dynamic estimation of COVID-19 pandemic in the presence of vaccinations and viral variants. By introducing the vaccinated compartment and re-infection factor into the classical susceptible, exposed, infectious, recovered, and deceased (SEIRD) model to characterise the vaccination and re-infection effects, a new vaccination-SEIRD (V-SEIRD) model is established to depict the dynamics of COVID-19 transmission in the presence of vaccinations and viral variants under the variable total population. Upon this model, an extended Kalman filter (EKF) is further developed to simultaneously estimate the model parameters and predict the transmission state for COVID-19 pandemic. Results demonstrate that the suggested approach is capable of characterising the vaccination and re-infection impacts on COVID-19 evolution, resulting in enhanced accuracy for COVID-19 prediction in the presence of vaccinations and viral variants. The proposed method can aid the design of vaccination strategies and public health policies for infectious disease prevention and control.

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引用次数: 0

Some energy-preserving schemes for fractional Hamiltonian system with fractional Laplacian

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2024-12-16 DOI: 10.1016/j.matcom.2024.12.005

Junjie Wang

In the paper, the energy-preserving scheme is presented for a class of fractional Hamiltonian system with fractional Laplacian. First, we show an equivalent form of the fractional Hamiltonian system by introducing some new auxiliary variables. The new system is discretized by the scalar auxiliary variable scheme in time, and a linear semi-discrete system is obtained, which can conserve the energy conservation law. Second, we show numerical schemes for one dimensional and two dimensional fractional Laplacian based on hyper-singular integral definition by quadratic interpolation function and linear interpolation function, and it finds that the differential matrices of the above schemes are symmetric Toeplitz matrices. Then, we use above scalar auxiliary variable scheme in time, and the above numerical scheme of fractional Laplacian in space to solve some fractional systems, and prove that the schemes can preserve energy conservation laws. Finally, the numerical experiments of some fractional Hamiltonian systems are given to verify the correctness of theoretical results.

引用次数: 0

Hopf-Hopf bifurcation and hysteresis in a COVID-19 transmission model implementing vaccination induced recovery and a modified Holling type-III treatment response

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2024-12-16 DOI: 10.1016/j.matcom.2024.12.009

Arpita Devi, Praveen Kumar Gupta

In times where treatment methods are overwhelmed and have reached a saturation state, it is necessary to examine the propagation patterns of COVID-19 to assist in the decision-making process. In light of its practical significance, this paper proposes a dynamical model while implementing vaccination of susceptibles and a modified Holling type - III treatment response in presence of waning immunity. The susceptible population is assumed to be vaccinated and are transferred to the recovered class. The model also accounts for the cases of imperfect vaccination resulting in the relapse of those individuals. To have a better comprehension of the new model, the non-negativity and boundedness of its solutions are studied. The model shows the presence of a maximum of three endemic equilibria along with a disease-free equilibrium. Transcritical bifurcation is evident for basic reproduction number greater than unity and there is the occurrence of Hopf bifurcation in the system via periodic oscillations. The direction of the Hopf bifurcation is supercritical and the unstable oscillations stabilize when the transmission rate increases. Formation of endemic bubbles in the system suggests the presence of Hopf-Hopf bifurcation. The model exhibits the phenomenon of forward hysteresis owing to the multistability of the endemic equilibria. Sensitivity analysis and data fitting illustrate the practical validity of the model along with numerical simulations. Based on these findings, the modified saturated treatment response is deemed valuable over the traditional response due to its practical relevance in the context of modern healthcare. With significant advancements in infrastructure, the limitations on medical resources are less pronounced, offering clearer insights into the evolving dynamics of COVID-19.

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引用次数: 0

Multi-strategy ensemble wind driven optimization algorithm for robot path planning

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2024-12-16 DOI: 10.1016/j.matcom.2024.11.023

Chao Zhang , Yi Yang , Wei Chen

In this study, a multi-strategy ensemble wind driven optimization (MEWDO) algorithm is proposed and combined with cubic spline interpolation to solve path planning challenges for single and multiple robots. The proposed MEWDO uses a Chebyshev map to initialize air particle populations and increase population diversity. A segmented learning local exploitation strategy is proposed to upgrade the exploitation ability of the algorithm. To enhance the exploration ability of the algorithm, a mutation strategy is introduced that disturbs dimensions one by one, based on the F-distribution with asymmetric characteristics. First, performance comparison experiments were conducted between MEWDO and seven other intelligent algorithms on 16 benchmark test functions. The results showed that MEWDO performed the best. Second, path planning simulation experiments were conducted in three static environments to compare MEWDO with three intelligent algorithms and the artificial potential field method, and MEWDO outperformed the comparison algorithms in terms of the planned shortest path and algorithm stability. In some complex rescue environments, multiple robots are frequently sent to perform tasks from different routes to improve the rescue success rate. For this purpose, MEWDO was used to plan task paths for five robots to test its performance in multi-robot path planning. The results showed that MEWDO finds the best route for all five robots to perform the task in a complex environment.

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引用次数: 0

Efficient spectral methods for the fourth-order elliptic eigenvalue problems

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2024-12-15 DOI: 10.1016/j.matcom.2024.12.006

Suna Ma , Huiyuan Li

An efficient spectral-Galerkin method for eigenvalue problems of the fourth-order elliptic equation on the unit ball is proposed in this paper. The efficiency of the method lies in the use of properly designed ball polynomials as basis functions. Error estimates for numerical eigenvalues and eigenvectors are conducted for the original fourth-order elliptic eigenvalue problem rather than the equivalent one-dimensional eigenvalue problem based on the pole condition in the literature. Numerical experiments are shown to demonstrate the efficiency of the algorithm and to validate the theoretical results.

引用次数: 0

On the stability preserving of L1 scheme to nonlinear time-fractional Schrödinger delay equations

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2024-12-13 DOI: 10.1016/j.matcom.2024.11.020

Zichen Yao, Zhanwen Yang, Lixin Cheng

In this paper, we investigate the stability preserving of L1 scheme to nonlinear time fractional Schrödinger delay equations. This kind of Schrödinger equation contains both nonlocal effect and time memory reaction term. We derive sufficient conditions to ensure the asymptotic stability of the analytical equations. After that, we approximate the equations via the Galerkin finite element method in space. We show that the semidiscrete numerical solutions can inherit the long time behavior of the solutions. After that, a fully discrete approximation of the equations is obtained by the L1 scheme and a linear interpolation procedure. We provide detailed estimations on the discrete operators that are obtained by the Z transform and its inverse. Together with a discrete fractional comparison principle, we prove that the L1 scheme preserves the stability of the underlying equations. The main results obtained in this work do not depend on spatial and temporal step sizes. A numerical example confirms the effectiveness of our derived method and validates the theoretical findings.

引用次数: 0

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