Pub Date : 2025-12-30DOI: 10.1016/j.cam.2025.117329
Jin Wen, Meng-Yao Zhou
This paper investigates the problem of simultaneously determining the initial value and initial velocity for the fractional diffusion-wave equation with singular perturbation, through the supplementary measurement data at two fixed time points. The paper derives the uniqueness of the solution to inverse problem by using the analytical and asymptotic characteristics of the Mittag-Leffler function, provided that the distance of these two time points is sufficiently small. In light of the problem’s ill-posedness, we adopt a boundary collocation method to solve this inverse problem, and use the Tikhonov regularization method combined with the GCV strategy. To demonstrate the efficiency and accuracy of our proposed method, we present several numerical examples in one-dimensional and two-dimensional cases.
{"title":"A regularization strategy for the backward problem for the fractional diffusion-wave equation with singular perturbation","authors":"Jin Wen, Meng-Yao Zhou","doi":"10.1016/j.cam.2025.117329","DOIUrl":"10.1016/j.cam.2025.117329","url":null,"abstract":"<div><div>This paper investigates the problem of simultaneously determining the initial value and initial velocity for the fractional diffusion-wave equation with singular perturbation, through the supplementary measurement data at two fixed time points. The paper derives the uniqueness of the solution to inverse problem by using the analytical and asymptotic characteristics of the Mittag-Leffler function, provided that the distance of these two time points is sufficiently small. In light of the problem’s ill-posedness, we adopt a boundary collocation method to solve this inverse problem, and use the Tikhonov regularization method combined with the GCV strategy. To demonstrate the efficiency and accuracy of our proposed method, we present several numerical examples in one-dimensional and two-dimensional cases.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117329"},"PeriodicalIF":2.6,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-29DOI: 10.1016/j.cam.2025.117326
Chunmei Wang , Shangyou Zhang
This paper introduces a novel weak Galerkin (WG) finite element method for the numerical solution of the Brinkman equations. The Brinkman model, which seamlessly integrates characteristics of both the Stokes and Darcy equations, is employed to describe fluid flow in multiphysics contexts, particularly within heterogeneous porous media exhibiting spatially variable permeability. The proposed WG method offers a unified and robust approach capable of accurately capturing both Stokes- and Darcy-dominated regimes. A discrete inf-sup condition is established, and optimal-order error estimates are rigorously proven for the WG finite element solutions. Furthermore, a series of numerical experiments is performed to corroborate the theoretical analysis, demonstrating the method’s accuracy and stability in addressing the complexities inherent in the Brinkman equations.
{"title":"Weak galerkin methods for the Brinkman equations","authors":"Chunmei Wang , Shangyou Zhang","doi":"10.1016/j.cam.2025.117326","DOIUrl":"10.1016/j.cam.2025.117326","url":null,"abstract":"<div><div>This paper introduces a novel weak Galerkin (WG) finite element method for the numerical solution of the Brinkman equations. The Brinkman model, which seamlessly integrates characteristics of both the Stokes and Darcy equations, is employed to describe fluid flow in multiphysics contexts, particularly within heterogeneous porous media exhibiting spatially variable permeability. The proposed WG method offers a unified and robust approach capable of accurately capturing both Stokes- and Darcy-dominated regimes. A discrete inf-sup condition is established, and optimal-order error estimates are rigorously proven for the WG finite element solutions. Furthermore, a series of numerical experiments is performed to corroborate the theoretical analysis, demonstrating the method’s accuracy and stability in addressing the complexities inherent in the Brinkman equations.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117326"},"PeriodicalIF":2.6,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-29DOI: 10.1016/j.cam.2025.117319
Yeliz Karaca, Majaz Moonis
<div><div>Mathematical dynamical ensemble modeling of neuron and neural network dynamics entails the precise capturing of the functions and complexities in multi-criteria decision-making processes while being capable of inferring and reconstructing the dynamics and structure of complex entities by serving the observability and evaluation emerging amid different flows of information. The complex dynamic system of the human brain encompasses the connections across neurons at various levels of granularity and connection characteristics. Stroke, one of the causes of morbidity and mortality worldwide, is among the most debilitating neurological diseases having a possible risk of loss of motor or cognitive function, causing long-term disability. Thus, stroke, which displays profound complexity and dynamic structures, requires timely intervention and heightened sensitivity in terms of capturing subtle details and findings. For predictive purposes in health-care systems under conditions dependent on time and highly complex, computing systems and Artificial Intelligence (AI) applications, with resilient, complex and informative properties, enable realization of intelligent properties alongside with facilitation and empowerment for accuracy in identification, detection, diagnosis, plan of treatment, follow-up processes and outcome prediction, where human knowledge, reasoning, intuition, experience and heuristics are essential. On the other hand, multifractal methods are utilized efficiently for the analyses of various complex systems with heterogeneous agents and investigation of multivariate datasets. In healthcare, it is essential to quantify the nonlinear brain dynamics and its anatomical structure to grasp its subtle features, and yet, since brain operates on multiple time-scales, this poses a formidable challenge considering its characterization across different interacting spatio-temporal scales involved. Characterized by a high degree of diagnostic complexity, neurological diseases require accurate prediction, individualized treatment and timely management. Across these strands, current study aims to facilitate multifaceted decision-making, optimized outcome prediction and tackle the complexity of stroke, which can result in accurate prediction and efficient management of the disease. To this end, the mathematical model proposed in this study has adopted the subsequent stages: (i) multifractal regularization method is applied to the stroke dataset (<em>X</em>), and by this application, the mf-stroke dataset <span><math><mrow><mo>(</mo><mover><mi>X</mi><mo>^</mo></mover><mo>)</mo></mrow></math></span> has been generated. (ii) ten different algorithms composed of deep learning methods, ensemble methods, fundamental methods and clustering methods are applied to the stroke dataset and generated mf-stroke dataset <span><math><mrow><mo>(</mo><mover><mi>X</mi><mo>^</mo></mover><mo>)</mo></mrow></math></span> (iii) the comparison of predictive accuracy rate
{"title":"Mathematical Neuron-Neural-Networks Dynamics Modeling and Brain Complexity of Multicriteria Fractal-Based Ensemble Predictive Algorithmic Systems","authors":"Yeliz Karaca, Majaz Moonis","doi":"10.1016/j.cam.2025.117319","DOIUrl":"10.1016/j.cam.2025.117319","url":null,"abstract":"<div><div>Mathematical dynamical ensemble modeling of neuron and neural network dynamics entails the precise capturing of the functions and complexities in multi-criteria decision-making processes while being capable of inferring and reconstructing the dynamics and structure of complex entities by serving the observability and evaluation emerging amid different flows of information. The complex dynamic system of the human brain encompasses the connections across neurons at various levels of granularity and connection characteristics. Stroke, one of the causes of morbidity and mortality worldwide, is among the most debilitating neurological diseases having a possible risk of loss of motor or cognitive function, causing long-term disability. Thus, stroke, which displays profound complexity and dynamic structures, requires timely intervention and heightened sensitivity in terms of capturing subtle details and findings. For predictive purposes in health-care systems under conditions dependent on time and highly complex, computing systems and Artificial Intelligence (AI) applications, with resilient, complex and informative properties, enable realization of intelligent properties alongside with facilitation and empowerment for accuracy in identification, detection, diagnosis, plan of treatment, follow-up processes and outcome prediction, where human knowledge, reasoning, intuition, experience and heuristics are essential. On the other hand, multifractal methods are utilized efficiently for the analyses of various complex systems with heterogeneous agents and investigation of multivariate datasets. In healthcare, it is essential to quantify the nonlinear brain dynamics and its anatomical structure to grasp its subtle features, and yet, since brain operates on multiple time-scales, this poses a formidable challenge considering its characterization across different interacting spatio-temporal scales involved. Characterized by a high degree of diagnostic complexity, neurological diseases require accurate prediction, individualized treatment and timely management. Across these strands, current study aims to facilitate multifaceted decision-making, optimized outcome prediction and tackle the complexity of stroke, which can result in accurate prediction and efficient management of the disease. To this end, the mathematical model proposed in this study has adopted the subsequent stages: (i) multifractal regularization method is applied to the stroke dataset (<em>X</em>), and by this application, the mf-stroke dataset <span><math><mrow><mo>(</mo><mover><mi>X</mi><mo>^</mo></mover><mo>)</mo></mrow></math></span> has been generated. (ii) ten different algorithms composed of deep learning methods, ensemble methods, fundamental methods and clustering methods are applied to the stroke dataset and generated mf-stroke dataset <span><math><mrow><mo>(</mo><mover><mi>X</mi><mo>^</mo></mover><mo>)</mo></mrow></math></span> (iii) the comparison of predictive accuracy rate","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"481 ","pages":"Article 117319"},"PeriodicalIF":2.6,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-29DOI: 10.1016/j.cam.2025.117325
Jie Shen , Jiwei Zhang , Chengchao Zhao
We consider in this paper a variable-step generalized second-order BDF scheme (VS-gBDF2) based on the Taylor expansion at time (ξ ≥ 1). Using the linear reaction-diffusion equation as an example, we investigate the numerical stability, convergence and computational efficiency of the proposed scheme for any ξ ≥ 1. We provide an asymptotically compatible analysis on the discrete energy dispassion law and establish stability and second-order convergence of the VS-gBDF2 scheme for any ξ ≥ 1. These results are proved under a restriction on the ratio of adjacent steps , where the upper bound and the lower bound rξ are dependent on the parameter ξ. The asymptotic compatibility means that the required ratio restriction will reduce to 0 < rk < rmax ≈ 4.8645 as ξ → 1, which is the ratio restriction for the classical variable-step BDF2 (VS-BDF2) given in (J. Math., 2021, 06:471-488). Numerical examples are provided to substantiate our theoretical analysis and validate the effectiveness of the adaptive time-step strategy. In particular, the proposed adaptive VS-gBDF2 schemes are shown to have stronger stability and higher efficiency than the classical () VS-BDF2 schemes when an appropriate value of ξ is chosen.
{"title":"Stability and convergence of a variable step generalized BDF2 scheme","authors":"Jie Shen , Jiwei Zhang , Chengchao Zhao","doi":"10.1016/j.cam.2025.117325","DOIUrl":"10.1016/j.cam.2025.117325","url":null,"abstract":"<div><div>We consider in this paper a variable-step generalized second-order BDF scheme (VS-gBDF2) based on the Taylor expansion at time <span><math><mrow><msub><mi>t</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>τ</mi><mi>n</mi></msub><mi>ξ</mi></mrow></math></span> (<em>ξ</em> ≥ 1). Using the linear reaction-diffusion equation as an example, we investigate the numerical stability, convergence and computational efficiency of the proposed scheme for any <em>ξ</em> ≥ 1. We provide an asymptotically compatible analysis on the discrete energy dispassion law and establish stability and second-order convergence of the VS-gBDF2 scheme for any <em>ξ</em> ≥ 1. These results are proved under a restriction on the ratio of adjacent steps <span><math><mrow><mn>0</mn><mo>≤</mo><msub><munder><mrow><mi>r</mi></mrow><mo>‾</mo></munder><mi>ξ</mi></msub><mo><</mo><msub><mi>r</mi><mi>k</mi></msub><mo><</mo><msub><mover><mi>r</mi><mo>¯</mo></mover><mi>ξ</mi></msub></mrow></math></span>, where the upper bound <span><math><msub><mover><mi>r</mi><mo>¯</mo></mover><mi>ξ</mi></msub></math></span> and the lower bound <u>r</u><sub><em>ξ</em></sub> are dependent on the parameter <em>ξ</em>. The asymptotic compatibility means that the required ratio restriction will reduce to 0 < <em>r<sub>k</sub></em> < <em>r</em><sub>max</sub> ≈ 4.8645 as <em>ξ</em> → 1, which is the ratio restriction for the classical variable-step BDF2 (VS-BDF2) given in (J. Math., 2021, 06:471-488). Numerical examples are provided to substantiate our theoretical analysis and validate the effectiveness of the adaptive time-step strategy. In particular, the proposed adaptive VS-gBDF2 schemes are shown to have stronger stability and higher efficiency than the classical (<span><math><mrow><mi>ξ</mi><mo>=</mo><mn>1</mn></mrow></math></span>) VS-BDF2 schemes when an appropriate value of <em>ξ</em> is chosen.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117325"},"PeriodicalIF":2.6,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-29DOI: 10.1016/j.cam.2025.117307
Jul Van den Broeck, Emile Vanderstraeten, Dries Vande Ginste
Owing to their increased electron mobility compared to conventional semiconductors, three-dimensional (3D) Dirac semimetals are considered to be promising candidates for integration into next-generation electronic devices. In these materials, the low-energy dynamics of the charge carriers are governed by an effective tilted Dirac equation, in which a mass term appears when strain is applied to the crystal lattice. In this work, we present a novel finite-difference scheme capable of numerically solving the 3D tilted Dirac equation in the time domain. The method employs fourth-order accurate finite differences to discretize the spatial derivatives and a symplectic partitioned Runge-Kutta (PRK) integrator to propagate the Dirac spinor in time. To this end, a careful separation of the complex-valued spinor into two real-valued parts is performed to ensure compatibility with the PRK technique. Moreover, to account for the additional term in the Hamiltonian arising from the tilt of the Dirac cones, fourth-order accurate averaging operators are incorporated into the spatial discretization, without compromising the key properties of the scheme. The resulting numerical method is explicit and is shown to conserve the norm, energy, and momentum of the system. Its stability condition is derived, and the numerical dispersion is thoroughly investigated. Illustrative numerical experiments are performed, demonstrating the excellent properties of the proposed method and its applicability to a more realistic scenario in which retroreflection is predicted to occur in the Dirac semimetal Cd3As2, as a result of its tilted dispersion relation.
{"title":"Conservative fourth-order accurate finite-difference scheme to solve the (3+1)D tilted Dirac equation in strained Dirac semimetals","authors":"Jul Van den Broeck, Emile Vanderstraeten, Dries Vande Ginste","doi":"10.1016/j.cam.2025.117307","DOIUrl":"10.1016/j.cam.2025.117307","url":null,"abstract":"<div><div>Owing to their increased electron mobility compared to conventional semiconductors, three-dimensional (3D) Dirac semimetals are considered to be promising candidates for integration into next-generation electronic devices. In these materials, the low-energy dynamics of the charge carriers are governed by an effective tilted Dirac equation, in which a mass term appears when strain is applied to the crystal lattice. In this work, we present a novel finite-difference scheme capable of numerically solving the 3D tilted Dirac equation in the time domain. The method employs fourth-order accurate finite differences to discretize the spatial derivatives and a symplectic partitioned Runge-Kutta (PRK) integrator to propagate the Dirac spinor in time. To this end, a careful separation of the complex-valued spinor into two real-valued parts is performed to ensure compatibility with the PRK technique. Moreover, to account for the additional term in the Hamiltonian arising from the tilt of the Dirac cones, fourth-order accurate averaging operators are incorporated into the spatial discretization, without compromising the key properties of the scheme. The resulting numerical method is explicit and is shown to conserve the norm, energy, and momentum of the system. Its stability condition is derived, and the numerical dispersion is thoroughly investigated. Illustrative numerical experiments are performed, demonstrating the excellent properties of the proposed method and its applicability to a more realistic scenario in which retroreflection is predicted to occur in the Dirac semimetal Cd<sub>3</sub>As<sub>2</sub>, as a result of its tilted dispersion relation.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117307"},"PeriodicalIF":2.6,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-29DOI: 10.1016/j.cam.2025.117315
Zhaohua Gong , Chongyang Liu , Benchawan Wiwatanapataphee , Yonghong Wu
This paper addresses the numerical solution issue for delay fractional optimal switched impulsive control problems. First, we formulate the delay fractional optimal switched impulsive control problem, in which the decision variables are the switching times together with the control parameters, and the cost function contains both the system’s cost at the switching times and the running cost defined by fractional integrals. Then, by making use of a novel time-scaling technique, this delay fractional optimal control problem is transformed to an equivalent problem with additional control parameters but fixed switching times. Furthermore, we present a discretization approach for the equivalent problem, which results in a series of discrete-time dynamic optimization problems. We also give the cost function’s left and right gradients, on which an algorithm is built for solving the resultant optimization problems. At last, two numerical examples are solved to validate the high effectiveness of the built optimization algorithm.
{"title":"Numerical computation of fractional optimal switched impulsive control problems with time-delay","authors":"Zhaohua Gong , Chongyang Liu , Benchawan Wiwatanapataphee , Yonghong Wu","doi":"10.1016/j.cam.2025.117315","DOIUrl":"10.1016/j.cam.2025.117315","url":null,"abstract":"<div><div>This paper addresses the numerical solution issue for delay fractional optimal switched impulsive control problems. First, we formulate the delay fractional optimal switched impulsive control problem, in which the decision variables are the switching times together with the control parameters, and the cost function contains both the system’s cost at the switching times and the running cost defined by fractional integrals. Then, by making use of a novel time-scaling technique, this delay fractional optimal control problem is transformed to an equivalent problem with additional control parameters but fixed switching times. Furthermore, we present a discretization approach for the equivalent problem, which results in a series of discrete-time dynamic optimization problems. We also give the cost function’s left and right gradients, on which an algorithm is built for solving the resultant optimization problems. At last, two numerical examples are solved to validate the high effectiveness of the built optimization algorithm.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117315"},"PeriodicalIF":2.6,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-28DOI: 10.1016/j.cam.2025.117257
Grigory Panasenko, Konstantin Pileckas
The stationary and non-stationary Navier-Stokes equations in a thin tube structure, with no slip boundary condition, are considered. A new method of partial asymptotic dimension reduction is introduced and justified by an error estimate. This method reduces the problem to a one-dimensional equation on the graph and several decoupled full dimension problems in small domains. The full dimension problems are independent and can be solved by parallel computing.
{"title":"Hybrid dimension modeling for Navier-Stokes equations in thin tube structures","authors":"Grigory Panasenko, Konstantin Pileckas","doi":"10.1016/j.cam.2025.117257","DOIUrl":"10.1016/j.cam.2025.117257","url":null,"abstract":"<div><div>The stationary and non-stationary Navier-Stokes equations in a thin tube structure, with no slip boundary condition, are considered. A new method of partial asymptotic dimension reduction is introduced and justified by an error estimate. This method reduces the problem to a one-dimensional equation on the graph and several decoupled full dimension problems in small domains. The full dimension problems are independent and can be solved by parallel computing.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117257"},"PeriodicalIF":2.6,"publicationDate":"2025-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article proposes a general framework of implicit Newmark-(γ, θ)-schemes for temporal discretization combined with weak Galerkin methods in spatial direction for the acoustic wave equations. Stability analysis of the corresponding complete discrete schemes is discussed, and it is shown that a particular family of the weak Galerkin based Newmark-(γ, θ)-schemes are discrete energy conserving. The optimum convergence of the error , where and k ≥ 1, in the L2-norm has been established. Finally, a rigorous numerical investigation was carried out exhibiting the efficacy and optimality of the proposed algorithm.
{"title":"Complete discrete error analysis of implicit Newmark-(γ, θ)-schemes for the acoustic wave equations with variable coefficients using weak Galerkin methods","authors":"Puspendu Jana, Achyuta Ranjan Dutta Mohapatra, Bhupen Deka","doi":"10.1016/j.cam.2025.117285","DOIUrl":"10.1016/j.cam.2025.117285","url":null,"abstract":"<div><div>This article proposes a general framework of implicit Newmark-(<em>γ, θ</em>)-schemes for temporal discretization combined with weak Galerkin methods in spatial direction for the acoustic wave equations. Stability analysis of the corresponding complete discrete schemes is discussed, and it is shown that a particular family of the weak Galerkin based Newmark-(<em>γ, θ</em>)-schemes are discrete energy conserving. The optimum convergence of the error <span><math><mrow><mi>O</mi><mo>(</mo><msup><mi>τ</mi><mi>α</mi></msup><mo>+</mo><msup><mi>h</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></math></span>, where <span><math><mrow><mi>α</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></mrow></math></span> and <em>k</em> ≥ 1, in the <em>L</em><sup>2</sup>-norm has been established. Finally, a rigorous numerical investigation was carried out exhibiting the efficacy and optimality of the proposed algorithm.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"481 ","pages":"Article 117285"},"PeriodicalIF":2.6,"publicationDate":"2025-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-28DOI: 10.1016/j.cam.2025.117320
Roberto Vila , Helton Saulo
In this paper, we introduce a novel flexible Gini index, referred to as the extended mth Gini index, which is defined through ordered differences between the jth and kth order statistics within subsamples of size m, for indices satisfying 1 ≤ j < k ≤ m. We derive a closed-form expression for the expectation of the corresponding estimator under the gamma distribution and prove its unbiasedness, thereby extending prior findings by [1], [2], and [3]. A Monte Carlo simulation illustrates the estimator’s finite-sample unbiasedness. A real data set on gross domestic product (GDP) per capita is analyzed to illustrate the proposed measure.
在本文中，我们引入了一种新的灵活的基尼指数，称为扩展的第m个基尼指数，它是通过大小为m的子样本内第j阶和第k阶统计量之间的有序差来定义的，对于满足1 ≤ j <； k ≤ m的指标。我们导出了相应估计量在gamma分布下的期望的封闭表达式，并证明了其无偏性，从而扩展了先前的发现[1]，[2]和[3]。蒙特卡罗模拟说明了估计器的有限样本无偏性。通过对人均国内生产总值（GDP）的实际数据集进行分析，以说明所提出的措施。
{"title":"An unbiased estimator of a novel extended mth Gini index for gamma distributed populations","authors":"Roberto Vila , Helton Saulo","doi":"10.1016/j.cam.2025.117320","DOIUrl":"10.1016/j.cam.2025.117320","url":null,"abstract":"<div><div>In this paper, we introduce a novel flexible Gini index, referred to as the extended <em>m</em>th Gini index, which is defined through ordered differences between the <em>j</em>th and <em>k</em>th order statistics within subsamples of size <em>m</em>, for indices satisfying 1 ≤ <em>j</em> < <em>k</em> ≤ <em>m</em>. We derive a closed-form expression for the expectation of the corresponding estimator under the gamma distribution and prove its unbiasedness, thereby extending prior findings by [1], [2], and [3]. A Monte Carlo simulation illustrates the estimator’s finite-sample unbiasedness. A real data set on gross domestic product (GDP) per capita is analyzed to illustrate the proposed measure.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117320"},"PeriodicalIF":2.6,"publicationDate":"2025-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-27DOI: 10.1016/j.cam.2025.117321
Samriti Chandel , Bhupendra Kumar Pathak , Gajendra K. Vishwakarma
As the rapid transition of automotive industry towards sustainable mobility, electric vehicles are in growing demand due to their environmental benefits and advanced technology. But considering the best electric vehicle among them is a complex decision due to lack of information, subjective judgment and variability which leads to uncertainty. To address this uncertainty q-rung orthopair fuzzy sets method is employed which is better than traditional fuzzy method. In this paper a novel entropy measure for q-rung orthopair fuzzy sets is proposed, with the goal of improving uncertainty handling in multi-criteria decision making issues. The Complex Proportional Assessment approach (COPRAS) is then used to evaluate and rank several electric vehicle choices based on the proposed entropy measure. Using the proposed method, we are able to identify the best electric vehicle according to one’s needs, the results are then compared with some existing entropy measure for the validation of proposed entropy and the results show that the new entropy offers ranks that are more dependable and consistent. The proposed entropy measure enhances the capability of q-rung orthopair fuzzy sets to model uncertainty and improves the accuracy of decision making when integrated with the COPRAS approach. It enables better differentiation among alternatives under uncertain and imprecise conditions based on the criteria for choosing best alternative.
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