Article
Mathematical & Computational Biology
Sarita Bugalia, Jai Prakash Tripathi, Hao Wang
Summary: This paper proposes a delayed SEIR epidemic model with intervention strategies and recovery under resource constraints. It is found that time delays change the system dynamics through Hopf bifurcation and oscillations, and the intervention strength and treatment limitations have significant impacts on infection levels. The study highlights the importance of considering time delays in intervention and recovery in epidemic models.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2021)
Article
Mathematics, Interdisciplinary Applications
Faris Alzahrani, Oyoon Abdul Razzaq, Daniyal Ur Rehman, Najeeb Alam Khan, Ali Saleh Alshomrani, Malik Zaka Ullah
Summary: Among the many factors affecting preventive interventions for infectious diseases, timely reporting to hospitals is crucial. However, many individuals fail to report, making it challenging for researchers to measure data and develop prevention strategies. This paper proposes a novel epidemic model that incorporates unreported individuals and utilizes fractional-order differential equations to enhance realism. Optimal control methods are applied to analyze the effectiveness of awareness campaigns in shifting unreported individuals to the reported class.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
Xuhui Li, Ranjit Kumar Upadhyay, Anwar Zeb, Zizhen Zhang
Summary: In this paper, a delayed smoking model with reversion class is proposed, and the local stability of the smoking equilibrium and Hopf bifurcation are analyzed by taking the time delay as the bifurcation parameter. Furthermore, the global exponential stability is proved using the linear matrix inequality method. Theoretical results are validated numerically and graphically.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics, Applied
Chandan Maji, Fahad Al Basir, Debasis Mukherjee, Kottakkaran Sooppy Nisar, Chokkalingam Ravichandran
Summary: This study proposes and analyzes a mathematical model for COVID-19 transmission influenced by awareness campaigns through social media. The existence and stability of equilibria, as well as the occurrence of Hopf bifurcation, are studied using qualitative theory. The study shows that public awareness plays a significant role in controlling the pandemic, and that time delay affects the system's stability.
Article
Biochemistry & Molecular Biology
Prakash Raj Murugadoss, Venkatesh Ambalarajan, Vinoth Sivakumar, Prasantha Bharathi Dhandapani, Dumitru Baleanu
Summary: This study aims to examine the transmission of dengue with a time delay by developing a dynamic model. The results showed that the stability of the illness-free equilibrium is not affected by the length of the time delay. However, Hopf bifurcation may occur depending on the impact of the delay on the equilibrium stability. Numerical simulations were conducted to validate the theoretical results. This mathematical modeling is effective for evaluating the recovery of a large population of afflicted individuals with a time delay.
FRONTIERS IN BIOSCIENCE-LANDMARK
(2023)
Article
Engineering, Multidisciplinary
Xiaomei Hu, A. Pratap, Zizhen Zhang, Aying Wan
Summary: Smoking has many harmful effects on the health and lives of smokers, as well as on public health. This paper investigates a delayed smoking model with different states of smokers and analyzes the stability of the model, as well as conducts numerical simulations to validate the theoretical results.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Mathematics, Interdisciplinary Applications
Swati Tyagi, Subash C. Martha, Syed Abbas, Amar Debbouche
Summary: This work discusses the modeling and surveillance of dynamics of infectious diseases, including early stage asymptomatic and later stage symptomatic infections. It emphasizes the conceptual ideas and mathematical tools needed for infectious disease modeling, computing the basic reproduction number and investigating the stability of equilibria. Numerical simulations are conducted to validate the derived results.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematical & Computational Biology
Zhenzhen Liao, Shujing Gao, Shuixian Yan, Genjiao Zhou
Summary: A mathematical model for the transmission dynamics of citrus Huanglongbing has been formulated in this paper, with the consideration of latent period as a time delay factor. The study showed that stability changes occur through Hopf bifurcation in the delayed system. Optimal control theory was applied to investigate the optimal strategy for curtailing the disease spread, suggesting that implementation of control techniques while minimizing the cost of implementation of optimal control strategies is feasible.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2021)
Article
Mathematics, Interdisciplinary Applications
Ashfaq Ahmad, Rashid Ali, Ijaz Ahmad, Fuad A. Awwad, Emad A. A. Ismail
Summary: This paper proposes a new model for HIV/AIDS and investigates its dynamical behavior by introducing new compartments. The steady-state solutions and threshold quantity R0 are calculated, showing the stability of the infection-free state. The conclusions are supported through numerical simulations and a comprehensive analysis of a fractional-order HIV model. The results provide valuable insights for designing effective control strategies.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Ruizhi Yang, Dan Jin, Wenlong Wang
Summary: This study incorporates time delay in the resource limitation of prey into a diffusive predator-prey model with a generalist predator. By analyzing the eigenvalue spectrum, the study investigates the instability and Hopf bifurcation induced by time delay. The normal form method and center manifold reduction for partial functional differential equation are utilized to obtain conditions for determining the bifurcation direction and stability of the bifurcating periodic solution. The results suggest that time delay can destabilize the coexisting equilibrium stability and induce bifurcating periodic solution when it exceeds a certain threshold.
Article
Mathematics, Interdisciplinary Applications
Ming Liu, Jun Cao, Xiaofeng Xu
Summary: This paper investigates the dynamics of a phytoplankton-zooplankton system with delay and diffusion. Using various methods, the study focuses on positivity, persistence, stability of steady states, as well as the existence of local Hopf bifurcation and global positive periodic solutions. Numerical simulations are conducted to illustrate the analytical results.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2021)
Article
Mathematics, Applied
Pegah Taghiei Karaji, Nemat Nyamoradi, Bashir Ahmad
Summary: In this paper, the SIR model with a nonlinear incidence rate is studied. The disease-free equilibrium E0, the endemic equilibrium E1, and the basic reproduction number R0 of the model are obtained. The local asymptotic stability of E0 is established when R0<1, and the local asymptotic stability of E1 is proved when R0>1. The global stability of the model is studied using Barbalat's lemma. The transcritical bifurcation analysis is investigated by the Sotomayor theorem. The existence of Hopf bifurcation and the sensitivity analysis of the basic reproduction number are checked. Numerical simulations are conducted to support the obtained results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematical & Computational Biology
Yu Yang, Gang Huang, Yueping Dong
Summary: This work focuses on an HIV infection model with intracellular delay and immune response delay. Sufficient criteria for the stability of equilibria and the existence of Hopf bifurcation are derived. The results show that the intracellular delay has no effect on the stability of the immunity-present equilibrium, while the immune response delay can destabilize it through Hopf bifurcation. Numerical simulations are provided to support the theoretical results.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2023)
Article
Mathematics, Interdisciplinary Applications
Jingnan Wang, Hongbin Shi, Li Xu, Lu Zang
Summary: This paper discusses a model of tumor and lymphatic immune system interaction with two time delays, analyzing the stability of equilibrium and the existence of Hopf bifurcations. The numerical simulations show different behaviors under various time delays, providing insights into the biomedical significance of tumor and T lymphocyte dynamics.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
Zizhen Zhang, Weishi Zhang, Kottakkaran Sooppy Nisar, Nadia Gul, Zahid Ahmed
Summary: This paper analyzes a mathematical model for malware dissemination on wireless sensor networks with time delay. The study focuses on local stability, Hopf bifurcation, and global exponential stability. Linear matrix inequality techniques are utilized to establish stability, while normal form theory and center manifold theorem are applied to study the properties of the Hopf bifurcation. A computer numerical simulation example is presented to validate the obtained results.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Mathematics, Applied
Shraddha Ramdas Bandekar, Mini Ghosh
Summary: This study provides a detailed analysis of the disease spread during the first and second waves of COVID-19 in India through numerical simulation, showcasing the importance of accurate lockdown strategies and sufficient medical care in reaching the peak of infections and observing a decline in cases afterward.
STOCHASTIC ANALYSIS AND APPLICATIONS
(2022)
Article
Automation & Control Systems
Hua-Cheng Zhou, Ze-Hao Wu, Bao-Zhu Guo, Yangquan Chen
Summary: This paper studies the boundary stabilization and disturbance rejection problem for an unstable time fractional diffusion-wave equation with Caputo time fractional derivative. State feedback control and output feedback control are proposed for the case of no boundary external disturbance, and a disturbance estimator and a new control law are designed for the case with boundary external disturbance. Rigorous mathematical proofs are presented.
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
(2022)
Article
Mathematics, Applied
I. R. Sofia, Mini Ghosh
Summary: In this study, a nonlinear mathematical model is formulated and analyzed to study the dynamics of smoking and its societal impact. The model considers different compartments representing potential smokers, occasional smokers, smokers, and quitters. The inclusion of smoking-related deaths and exploration of parameter impacts on equilibrium levels provide insights into understanding and addressing smoking habits.
STOCHASTIC ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematical & Computational Biology
Shraddha Ramdas Bandekar, Mini Ghosh, C. Rajivganthi
Summary: The arrival of a new disease has caused widespread destruction of human lives and the economy for a year. COVID-19, a pandemic, has claimed millions of lives. This study develops an epidemiological model with vaccination to analyze the significance of higher vaccination efficacy and population vaccination rate in controlling the rise in infections and preventing premature deaths. The study emphasizes that vaccination alone is not enough to eradicate the virus, and vaccine efficacy and other interventions play a crucial role.
INTERNATIONAL JOURNAL OF BIOMATHEMATICS
(2023)
Article
Automation & Control Systems
Wen Kang, Xiao-Nan Wang, Bao-Zhu Guo
Summary: This work proposes an observer-based fuzzy quantized control method for stochastic third-order parabolic partial differential equations (PDEs). The method introduces three types of quantizers and reduces the energy consumption of the system. Different stability results are presented for each case, and sufficient LMI-based conditions are investigated to ensure the stability and performance of the system.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2023)
Article
Automation & Control Systems
Hongyinping Feng, Bao-Zhu Guo
Summary: This paper designs an observer for SISO linear finite-dimensional systems corrupted by general disturbances. The proposed observer, called extended dynamics observer (EDO), can estimate both state and disturbance simultaneously. The observer design assumes that the plant with unknown disturbance is observable. The main advantage of this method is the maximum utilization of prior information of the disturbance. The well-posedness of EDO is established and the theoretical results are validated by numerical simulations. (c) 2023 European Control Association. Published by Elsevier Ltd. All rights reserved.
EUROPEAN JOURNAL OF CONTROL
(2023)
Article
Automation & Control Systems
Ze-Hao Wu, Hua-Cheng Zhou, Feiqi Deng, Bao-Zhu Guo
Summary: In this article, a novel control strategy, disturbance observer-based control, is applied to stabilize and reject disturbances in an antistable stochastic heat equation with boundary actuation and unknown external disturbance. The control design uses a disturbance observer to estimate and reject the unknown disturbance, and attenuates the in-domain multiplicative noise. The stability of the resulting closed-loop system is demonstrated. A numerical example validates the effectiveness of the proposed control approach.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2023)
Article
Automation & Control Systems
Tingting Meng, Bao-Zhu Guo
Summary: In this article, we address the problem of robust output regulation for an MIMO wave system with disturbance and reference from an exosystem. We propose an observer-based approach from the perspective of partial differential equations (PDEs). The main differences from previous works lie in our consideration of exosystems with non-algebraically simple eigenvalues and the direct design of tracking error feedback controls from the uncertain PDEs themselves. We introduce transformations to convert the original system into a disturbance-free system and each reference into a linear combination of the exosystem, allowing for the design of an observer and feedforward controls. The robustness of the closed-loop system is discussed through stability analysis.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2023)
Article
Mathematics, Applied
Fu Zheng, Sijia Zhang, Huakun Wang, Bao-Zhu Guo
Summary: In this paper, the exponential stabilization problem of a heat-wave coupled system under boundary control and collocated observation is considered. Two kinds of feedback strategies, namely static negative proportional feedback and dynamic feedback, are designed. The exponential stabilities of the closed-loop systems under different feedbacks are verified using the Lyapunov function direct method. The H infinity robustness is further analyzed and related sufficient conditions are developed. Additionally, the closed-loop systems are discretized into semi-discrete systems using a new finite difference method, and the uniform exponential stabilities of the discrete systems are established using an approach paralleling the continuous counterpart.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Nurehemaiti Yiming, Bao-Zhu Guo
Summary: In this paper, the asymptotic behavior of an M/G/1 retrial queueing system with server breakdowns is studied, and it is described by infinitely many partial integro-differential equations. The stability and convergence properties of the system are analyzed through the investigation of the system operator's spectrum. The results show the strong stability of the time-dependent solution in the natural Banach state space and the convergence of the solution to its steady-state solution when the server failure rate is zero. Additionally, the properties of the system operator and the corresponding C0-semigroup are examined.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Automation & Control Systems
Mengling Li, Ze-Hao Wu, Feiqi Deng, Bao-Zhu Guo
Summary: In this article, the active disturbance rejection control approach is applied for the first time to address the disturbance rejection and consensus problems in a class of second-order stochastic multiagent systems with undirected and connected network topology. Extended state observers are designed to estimate the unmeasured states and random total disturbance, and active antidisturbance consensus protocols are proposed to achieve consensus in mean square and almost sure practical sense. Numerical simulations are conducted to validate the effectiveness of the consensus protocols.
IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS
(2023)
Article
Automation & Control Systems
Bao-Zhu Guo, Hao-Lan Peng, Ze-Hao Wu
Summary: In this paper, the convergence of a nonlinear tracking differentiator constructed from a finite-time stable system is considered in the presence of bounded stochastic noise. The existence of global weak solutions is proved, and it is shown that the nonlinear tracking differentiator tracks the input signal in the almost surely practical sense. The convergence accuracy of the proposed differentiator is demonstrated to be higher than that of the linear tracking differentiator with the same tuning parameter through numerical simulations.
IFAC JOURNAL OF SYSTEMS AND CONTROL
(2023)
Article
Automation & Control Systems
Zhi-Liang Zhao, Ruonan Yuan, Bao-Zhu Guo, Zhong-Ping Jiang
Summary: This paper considers the finite-time stabilization problem for a class of multi-input multi-output nonlinear systems composed of several different subsystems. It presents a novel decentralized, continuous finite-time output-feedback control algorithm by compensating the unknown nonlinear couplings and applying a saturation technique. The effectiveness of the proposed design is validated through rigorous mathematical analysis and numerical simulations.
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2023)
Article
Automation & Control Systems
Qiaomin Xiang, Ze-Hao Wu, Ju H. Parks, Bao-Zhu Guo
Summary: This paper investigates the observability and observer design for a class of systems described by two-dimensional hyperbolic PDEs with superlinear boundary conditions that can exhibit chaos. The exact and approximate observability are proven using the method of characteristic and boundary reflection relations. Based on observability, two types of Luenberger PDE observers are designed, using boundary velocity and boundary displacement measurements respectively. Sufficient conditions are developed to guarantee the global exponential stability and global asymptotic stability of the observer error systems. Numerical simulations are conducted to validate the theoretical findings.
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2023)
Article
Physics, Multidisciplinary
Shraddha Ramdas Bandekar, Mini Ghosh, Kaiming Bi
Summary: In this study, a deterministic model is developed to study the impact of COVID-19 disease transmission considering high-risk and low-risk susceptible population. The model is an extension of SEIR model and includes cross infection between high-risk and low-risk population. The model is also modified to see the impact of antimicrobial resistance in the infected population. Furthermore, an optimal control model is developed to incorporate control strategies and evaluate their impact on the infected population.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Mathematics, Applied
M. S. Bruzon, T. M. Garrido, R. de la Rosa
Summary: We study a family of generalized Zakharov-Kuznetsov modified equal width equations in (2+1)-dimensions involving an arbitrary function and three parameters. By using the Lie group theory, we classify the Lie point symmetries of these equations and obtain exact solutions. We also show that this family of equations admits local low-order multipliers and derive all local low-order conservation laws through the multiplier approach.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Dohee Jung, Changbum Chun
Summary: The paper presents a general approach to enhance the Pade iterations for computing the matrix sign function by selecting an arbitrary three-point family of methods based on weight functions. The approach leads to a multi-parameter family of iterations and allows for the discovery of new methods. Convergence and stability analysis as well as numerical experiments confirm the improved performance of the new methods.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Abhishek Yadav, Amit Setia, M. Thamban Nair
Summary: In this paper, we propose a Galerkin's residual-based numerical scheme for solving a system of Cauchy-type singular integral equations using Chebyshev polynomials. We prove the well-posedness of the system and derive a theoretical error bound and convergence order. The numerical examples validate the theoretical results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Fernando Chacon-Gomez, M. Eugenia Cornejo, Jesus Medina, Eloisa Ramirez-Poussa
Summary: The use of decision rules allows for reliable extraction of information and inference of conclusions from relational databases, but the concepts of decision algorithms need to be extended in fuzzy environments.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Ilhame Amirali, Gabil M. Amiraliyev
Summary: This paper considers the one-dimensional initial-boundary problem for a pseudoparabolic equation with a time delay. To solve this problem numerically, a higher-order difference method is constructed and the error estimate for its solution is obtained. Based on the method of energy estimates, the fully discrete scheme is shown to be convergent of order four in space and of order two in time. The given numerical results illustrate the convergence and effectiveness of the numerical method.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Tong-tong Shang, Guo-ji Tang, Wen-sheng Jia
Summary: The goal of this paper is to investigate a class of linear complementarity problems over tensor-spaces, denoted by TLCP, which is an extension of the classical linear complementarity problem. First, two classes of structured tensors over tensor-spaces (i.e., T-R tensor and T-RO tensor) are introduced and some equivalent characterizations are discussed. Then, the lower bound and upper bound of the solutions in the sense of the infinity norm of the TLCP are obtained when the problem has a solution.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Fabio Difonzo, Pawel Przybylowicz, Yue Wu
Summary: This paper focuses on the existence, uniqueness, and approximation of solutions of delay differential equations (DDEs) with Caratheodory type right-hand side functions. It presents the construction of the randomized Euler scheme for DDEs and investigates its error. Furthermore, the paper reports the results of numerical experiments.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Priyanka Roy, Geetanjali Panda, Dong Qiu
Summary: In this article, a gradient based descent line search scheme is proposed for solving interval optimization problems under generalized Hukuhara differentiability. The innovation and importance of these concepts are presented from practical and computational perspectives. The necessary condition for existence of critical point is presented in inclusion form of interval-valued gradient. Suitable efficient descent direction is chosen based on the monotonic property of the interval-valued function and specific interval ordering. Mathematical convergence of the scheme is proved under the assumption of Inexact line search. The theoretical developments are implemented with a set of interval test problems in different dimensions. A possible application in finance is provided and solved by the proposed scheme.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Zhongqian Wang, Changqing Ye, Eric T. Chung
Summary: In this paper, the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with mixed boundary conditions for elasticity equations in high contrast media is developed. The method offers advantages such as independence of target region's contrast from precision and significant impact of oversampling domain sizes on numerical accuracy. Furthermore, this is the first proof of convergence of CEM-GMsFEM with mixed boundary conditions for elasticity equations. Numerical experiments demonstrate the method's performance.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Samaneh Soradi-Zeid, Maryam Alipour
Summary: The Laguerre polynomials are a new set of basic functions used to solve a specific class of optimal control problems specified by integro-differential equations, namely IOCP. The corresponding operational matrices of derivatives are calculated to extend the solution of the problem in terms of Laguerre polynomials. By considering the basis functions and using the collocation method, the IOCP is simplified into solving a system of nonlinear algebraic equations. The proposed method has been proven to have an error bound and convergence analysis for the approximate optimal value of the performance index. Finally, examples are provided to demonstrate the validity and applicability of this technique.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Almudena P. Marquez, Maria L. Gandarias, Stephen C. Anco
Summary: A generalization of the KP equation involving higher-order dispersion is studied. The Lie point symmetries and conservation laws of the equation are obtained using Noether's theorem and the introduction of a potential. Sech-type line wave solutions are found and their features, including dark solitary waves on varying backgrounds, are discussed.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Susanne Saminger-Platz, Anna Kolesarova, Adam Seliga, Radko Mesiar, Erich Peter Klement
Summary: In this article, we study real functions defined on the unit square satisfying basic properties and explore the conditions for generating bivariate copulas using parameterized transformations and other constructions.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Lulu Tian, Nattaporn Chuenjarern, Hui Guo, Yang Yang
Summary: In this paper, a new local discontinuous Galerkin (LDG) algorithm is proposed to solve the incompressible Euler equation in two dimensions on overlapping meshes. The algorithm solves the vorticity, velocity field, and potential function on different meshes. The method employs overlapping meshes to ensure continuity of velocity along the interfaces of the primitive meshes, allowing for the application of upwind fluxes. The article introduces two sufficient conditions to maintain the maximum principle of vorticity.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Cheng Wang, Jilu Wang, Steven M. Wise, Zeyu Xia, Liwei Xu
Summary: In this paper, a temporally second-order accurate numerical scheme for the Cahn-Hilliard-Magnetohydrodynamics system of equations is proposed and analyzed. The scheme utilizes a modified Crank-Nicolson-type approximation for time discretization and a mixed finite element method for spatial discretization. The modified Crank-Nicolson approximation allows for mass conservation and energy stability analysis. Error estimates are derived for the phase field, velocity, and magnetic fields, and numerical examples are presented to validate the proposed scheme's theoretical results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Mingyu He, Wenyuan Liao
Summary: This paper presents a numerical method for solving reaction-diffusion equations in spatially heterogeneous domains, which are commonly used to model biological applications. The method utilizes a fourth-order compact alternative directional implicit scheme based on Pade approximation-based operator splitting techniques. Stability analysis shows that the method is unconditionally stable, and numerical examples demonstrate its high efficiency and high order accuracy in both space and time.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
