Journal of Computational and Applied Mathematics最新文献

英文中文

An expanded mixed finite element method for fourth-order hyperbolic equations with variable coefficients 变系数四阶双曲型方程的扩展混合有限元法

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-12-22 DOI: 10.1016/j.cam.2025.117305

Wenhui Ma, Zhe Yin, Ailing Zhu

The fourth-order hyperbolic equation with variable coefficients can be used to describe complex vibration, wave and other phenomena, and it is widely applied in physics and engineering technology. In this paper, we study the expanded mixed finite element method for fourth-order hyperbolic equations with variable coefficients. By introducing two intermediate variables, the fourth-order differential equation is transformed into a system of lower-order partial differential equations. The semi-discrete expanded mixed finite element scheme is constructed, and the existence and uniqueness of the solution of the scheme are proved. The error estimates are analyzed by using the elliptic projection and L²-operator. We use the central difference to discretize the time derivative terms, establish the fully discrete expanded mixed finite element scheme, and prove the stability and convergence of the scheme. By comparing the expanded mixed finite element method with the standard mixed finite element method through a numerical example, the feasibility of the expanded mixed finite element method for solving differential equations with a small coefficient is verified. The correctness of the theoretical analysis is verified by numerically solving spatial one-dimensional and two-dimensional fourth-order hyperbolic equations with variable coefficients. The effect of the damping coefficient on the vibration is simulated.

变系数四阶双曲方程可以用来描述复杂的振动、波动等现象，在物理和工程技术中有着广泛的应用。本文研究了四阶变系数双曲型方程的扩展混合有限元法。通过引入两个中间变量，将四阶微分方程转化为一组低阶偏微分方程。构造了半离散扩展混合有限元格式，并证明了该格式解的存在唯一性。利用椭圆投影和l2算子对误差估计进行了分析。利用中心差分对时间导数项进行离散化，建立了完全离散的扩展混合有限元格式，并证明了该格式的稳定性和收敛性。通过数值算例将扩展混合有限元法与标准混合有限元法进行比较，验证了扩展混合有限元法求解小系数微分方程的可行性。通过对空间一维和二维四阶变系数双曲方程的数值求解，验证了理论分析的正确性。模拟了阻尼系数对振动的影响。

{"title":"An expanded mixed finite element method for fourth-order hyperbolic equations with variable coefficients","authors":"Wenhui Ma, Zhe Yin, Ailing Zhu","doi":"10.1016/j.cam.2025.117305","DOIUrl":"10.1016/j.cam.2025.117305","url":null,"abstract":"<div><div>The fourth-order hyperbolic equation with variable coefficients can be used to describe complex vibration, wave and other phenomena, and it is widely applied in physics and engineering technology. In this paper, we study the expanded mixed finite element method for fourth-order hyperbolic equations with variable coefficients. By introducing two intermediate variables, the fourth-order differential equation is transformed into a system of lower-order partial differential equations. The semi-discrete expanded mixed finite element scheme is constructed, and the existence and uniqueness of the solution of the scheme are proved. The error estimates are analyzed by using the elliptic projection and <em>L</em><sup>2</sup>-operator. We use the central difference to discretize the time derivative terms, establish the fully discrete expanded mixed finite element scheme, and prove the stability and convergence of the scheme. By comparing the expanded mixed finite element method with the standard mixed finite element method through a numerical example, the feasibility of the expanded mixed finite element method for solving differential equations with a small coefficient is verified. The correctness of the theoretical analysis is verified by numerically solving spatial one-dimensional and two-dimensional fourth-order hyperbolic equations with variable coefficients. The effect of the damping coefficient on the vibration is simulated.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"481 ","pages":"Article 117305"},"PeriodicalIF":2.6,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886356","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}

引用次数: 0

Portfolio selection based on the Herd Behavior Index 基于羊群行为指数的投资组合选择

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-12-22 DOI: 10.1016/j.cam.2025.117261

Wing Fung Chong , Churui Li , Daniël Linders

In this paper, we determine optimal portfolios using the Herd Behavior Index (HIX, [1]). HIX is a diversification measure that provides information about the extent to which stock prices move together in the same direction. The optimal minimum-HIX, as well as mean-HIX, portfolio can be seen as the most diversified one since it has the lowest degree of co-movement. We employ a reformulation method for determining the minimum-HIX, and mean-HIX, portfolio, as their closed-form expressions are not readily available in a general setting. This also allows us to study the mean-HIX efficient frontier. We prove the existence of the minimum-HIX, and mean-HIX, portfolio in the general setting, and provide their closed-form expressions in the two-stock case. We also study how to determine the minimum-HIX, as well as mean-HIX, portfolio when short-selling is allowed. This requires us to generalize the definition of HIX in order to ensure that the theoretically comonotonic portfolio always exceeds the actual portfolio in convex order for its return.

在本文中，我们使用羊群行为指数（HIX,[1]）确定最优投资组合。HIX是一种多元化指标，它提供了有关股价在同一方向上共同变动的程度的信息。最佳最小hix，以及平均hix，可以被视为最多样化的投资组合，因为它具有最低程度的共同运动。我们采用一种重新制定的方法来确定最小hix和平均hix投资组合，因为它们的封闭形式表达式在一般情况下不易获得。这也允许我们研究均值- hix效率边界。证明了一般情况下最小- hix和平均- hix组合的存在性，并给出了它们在双股情况下的封闭表达式。我们还研究了在允许卖空时如何确定最小hix值和平均hix值。这就要求我们对HIX的定义进行推广，以保证理论上的共单调投资组合的收益总是在凸序上超过实际的投资组合。

引用次数: 0

Tamed milstein scheme for stochastic differential equations with markovian switching with super-linear drift and diffusion coefficients 具有超线性漂移和扩散系数的马尔可夫切换随机微分方程的tame milstein格式

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-12-22 DOI: 10.1016/j.cam.2025.117306

Tejinder Kumar

We introduce a tamed Milstein scheme for stochastic differential equations with Markovian switching, specifically tailored for cases where both the drift and diffusion coefficients exhibit super-linear growth. We establish the moment stability of the proposed scheme and prove that it achieves a strong convergence rate of 1.0 in the

L^{p}

-sense, even when the coefficients are non-globally Lipschitz and grow super-linearly.

我们为具有马尔可夫切换的随机微分方程引入了一个驯服的Milstein格式，专门针对漂移系数和扩散系数都表现出超线性增长的情况量身定制。我们建立了该方案的矩稳定性，并证明了该方案在lp意义上具有1.0的强收敛速率，即使系数是非全局Lipschitz和超线性增长时也是如此。

引用次数: 0

Optimal L2 error estimates of a decoupled FEM for the Cahn-Hilliard-Navier-Stokes equations Cahn-Hilliard-Navier-Stokes方程解耦FEM的最优L2误差估计

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-12-21 DOI: 10.1016/j.cam.2025.117273

Haijun Gao , Xi Li , Zeyu Xia , Minfu Feng

This paper presents a decoupled, first-order, fully discrete finite element scheme for the Cahn–Hilliard–Navier–Stokes equations. The method is structured into three steps. The first step involves computing the Cahn–Hilliard equations, where the nonlinear term is treated with the convex splitting technique and the coupled part is handled by using an implicit-explicit scheme. Next, the pressure and velocity fields are decoupled through the pressure-correction method in the Navier–Stokes equations, thus achieving full decoupled between the Cahn–Hilliard and Navier–Stokes equations and enhancing computational efficiency. We have rigorously proved that the proposed scheme satisfies the existence and uniqueness of discrete scheme solutions and the discrete energy dissipation law. Furthermore, we developed a novel projection operator and derive the optimal L² error estimate for the fully discrete scheme. Therefore, we present the optimal L² error estimates for the phase field, chemical potential, velocity, and pressure in the finite element space. Numerical experiments verify the accuracy, efficiency, and theoretical results of the proposed scheme, confirming its unconditional stability.

本文给出了Cahn-Hilliard-Navier-Stokes方程的解耦一阶全离散有限元格式。该方法分为三个步骤。第一步涉及计算Cahn-Hilliard方程，其中非线性项采用凸分裂技术处理，耦合部分采用隐显格式处理。接下来，通过Navier-Stokes方程中的压力校正方法将压力场和速度场解耦，从而实现Cahn-Hilliard方程和Navier-Stokes方程的完全解耦，提高计算效率。我们严格地证明了所提出的格式满足离散格式解的存在唯一性和离散能量耗散律。此外，我们开发了一种新的投影算子，并推导了完全离散格式的最优L2误差估计。因此，我们提出了在有限元空间中相场、化学势、速度和压力的最佳L2误差估计。数值实验验证了该方案的精度、效率和理论结果，并证实了该方案的无条件稳定性。

{"title":"Optimal L2 error estimates of a decoupled FEM for the Cahn-Hilliard-Navier-Stokes equations","authors":"Haijun Gao , Xi Li , Zeyu Xia , Minfu Feng","doi":"10.1016/j.cam.2025.117273","DOIUrl":"10.1016/j.cam.2025.117273","url":null,"abstract":"<div><div>This paper presents a decoupled, first-order, fully discrete finite element scheme for the Cahn–Hilliard–Navier–Stokes equations. The method is structured into three steps. The first step involves computing the Cahn–Hilliard equations, where the nonlinear term is treated with the convex splitting technique and the coupled part is handled by using an implicit-explicit scheme. Next, the pressure and velocity fields are decoupled through the pressure-correction method in the Navier–Stokes equations, thus achieving full decoupled between the Cahn–Hilliard and Navier–Stokes equations and enhancing computational efficiency. We have rigorously proved that the proposed scheme satisfies the existence and uniqueness of discrete scheme solutions and the discrete energy dissipation law. Furthermore, we developed a novel projection operator and derive the optimal <em>L</em><sup>2</sup> error estimate for the fully discrete scheme. Therefore, we present the optimal <em>L</em><sup>2</sup> error estimates for the phase field, chemical potential, velocity, and pressure in the finite element space. Numerical experiments verify the accuracy, efficiency, and theoretical results of the proposed scheme, confirming its unconditional stability.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"481 ","pages":"Article 117273"},"PeriodicalIF":2.6,"publicationDate":"2025-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885863","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}

引用次数: 0

A least-squares virtual element method on polytopal mesh for a curl-div system 基于最小二乘虚元法的卷分割系统多边形网格

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-12-21 DOI: 10.1016/j.cam.2025.117275

Huoyuan Duan , Duowei Zhu

A new virtual element method of least-squares type is proposed for numerically solving a curl-div system, which typically arises from the magnetostatic problem. We employ the nodal virtual elements on polytopal meshes. With the Helmholtz L²-orthogonal decomposition and the related regular-singular decomposition, we develop a rigorous argument for proving the L²-coercivity. For the k (k ≥ 1) order virtual element which has the degrees of freedom in the interiors of the element faces, we strictly establish the optimal error estimates O(h^r) for the singular solution which has a low regularity and only belongs to (H^r(Ω))^d,

d = 2, 3

, for 1/2 < r < 1. For higher-order regularity solution, L²-norm

O (h^{k + 1})

optimal convergence can hold for k ≥ 1. Numerical results are provided.

提出了一种新的最小二乘型虚元法，用于数值求解一类典型的由静磁问题引起的旋流分型系统。我们在多边形网格上采用了节点虚元。利用Helmholtz l2 -正交分解和相应的正则-奇异分解，给出了证明l2 -矫顽力的一个严密的论证。对于在单元面内部具有自由度的k （k ≥ 1）阶虚元，对于1/2 <； r <； 1，正则性较低且只属于（hr （Ω））d, d=2,3的奇异解，严格建立了最优误差估计O（hr）。对于高阶正则解，当k ≥ 1时，l2范数O（hk+1）最优收敛成立。给出了数值结果。

{"title":"A least-squares virtual element method on polytopal mesh for a curl-div system","authors":"Huoyuan Duan , Duowei Zhu","doi":"10.1016/j.cam.2025.117275","DOIUrl":"10.1016/j.cam.2025.117275","url":null,"abstract":"<div><div>A new virtual element method of least-squares type is proposed for numerically solving a curl-div system, which typically arises from the magnetostatic problem. We employ the nodal virtual elements on polytopal meshes. With the Helmholtz <em>L</em><sup>2</sup>-orthogonal decomposition and the related regular-singular decomposition, we develop a rigorous argument for proving the <em>L</em><sup>2</sup>-coercivity. For the <em>k</em> (<em>k</em> ≥ 1) order virtual element which has the degrees of freedom in the interiors of the element faces, we strictly establish the optimal error estimates <em>O</em>(<em>h<sup>r</sup></em>) for the singular solution which has a low regularity and only belongs to (<em>H<sup>r</sup></em>(Ω))<sup><em>d</em></sup>, <span><math><mrow><mi>d</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow></math></span>, for 1/2 < <em>r</em> < 1. For higher-order regularity solution, <em>L</em><sup>2</sup>-norm <span><math><mrow><mi>O</mi><mo>(</mo><msup><mi>h</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></math></span> optimal convergence can hold for <em>k</em> ≥ 1. Numerical results are provided.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"481 ","pages":"Article 117275"},"PeriodicalIF":2.6,"publicationDate":"2025-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145842395","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}

引用次数: 0

Numerical solution to the three-dimensional p-Laplace equation: Finite difference methods and biological applications 三维p-拉普拉斯方程的数值解：有限差分法及其生物学应用

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-12-21 DOI: 10.1016/j.cam.2025.117270

Matthias Dogbatsey , Zhan Chen , Yuanzhen Shao , Shan Zhao

Solving the nonlinear and degenerate p-Laplace equation numerically is highly challenging, yet it has numerous applications across various fields. In this work, we propose and explore numerical schemes, including Picard’s Iteration scheme, Crank-Nicolson (CN) method, and Alternating Direction Implicit (ADI) scheme, for solving the p-Laplace equation in

R^{3}

for p ∈ [1, 2), aiming to identify the most effective numerical approaches within the framework of finite difference methods. In the existing literature, studies on the parabolic p-Laplace equation primarily consider the Cauchy problem with p ≥ 2. Our study bridges this gap by examining the parabolic p-Laplace equation for p ∈ [1, 2). To our knowledge, this is the first comprehensive study on the three-dimensional (3D) case. Our results demonstrate that the ADI scheme is the most efficient among the proposed 3D numerical schemes as it requires the least computational time while maintaining comparable accuracy in both analytical tests and solvation energy calculations. Moreover, we numerically verify that the solution of the pseudo-time parabolic p-Laplace equation converges to the solution of the corresponding highly nonlinear elliptic p-Laplace equation.

用数值方法求解非线性退化p-拉普拉斯方程是一个极具挑战性的问题，但它在各个领域都有广泛的应用。在这项工作中，我们提出并探索了用于求解p ∈ 中的p- laplace方程的数值格式，包括Picard的迭代格式，Crank-Nicolson （CN）方法和交替方向隐式（ADI）格式[1,2]，旨在确定有限差分方法框架内最有效的数值方法。在现有文献中，对抛物型p- laplace方程的研究主要考虑p ≥ 2的Cauchy问题。我们的研究通过检查p ∈ 的抛物型p-拉普拉斯方程来弥补这一差距[1,2]。据我们所知，这是第一次对三维（3D）病例进行全面研究。我们的结果表明，ADI方案是提出的3D数值方案中最有效的，因为它需要最少的计算时间，同时在分析测试和溶剂化能计算中保持相当的精度。此外，我们用数值方法验证了伪时间抛物型p-拉普拉斯方程的解收敛于相应的高度非线性椭圆型p-拉普拉斯方程的解。

{"title":"Numerical solution to the three-dimensional p-Laplace equation: Finite difference methods and biological applications","authors":"Matthias Dogbatsey , Zhan Chen , Yuanzhen Shao , Shan Zhao","doi":"10.1016/j.cam.2025.117270","DOIUrl":"10.1016/j.cam.2025.117270","url":null,"abstract":"<div><div>Solving the nonlinear and degenerate <em>p</em>-Laplace equation numerically is highly challenging, yet it has numerous applications across various fields. In this work, we propose and explore numerical schemes, including Picard’s Iteration scheme, Crank-Nicolson (CN) method, and Alternating Direction Implicit (ADI) scheme, for solving the <em>p</em>-Laplace equation in <span><math><msup><mi>R</mi><mn>3</mn></msup></math></span> for <em>p</em> ∈ [1, 2), aiming to identify the most effective numerical approaches within the framework of finite difference methods. In the existing literature, studies on the parabolic <em>p</em>-Laplace equation primarily consider the Cauchy problem with <em>p</em> ≥ 2. Our study bridges this gap by examining the parabolic <em>p</em>-Laplace equation for <em>p</em> ∈ [1, 2). To our knowledge, this is the first comprehensive study on the three-dimensional (3D) case. Our results demonstrate that the ADI scheme is the most efficient among the proposed 3D numerical schemes as it requires the least computational time while maintaining comparable accuracy in both analytical tests and solvation energy calculations. Moreover, we numerically verify that the solution of the pseudo-time parabolic <em>p</em>-Laplace equation converges to the solution of the corresponding highly nonlinear elliptic <em>p</em>-Laplace equation.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"481 ","pages":"Article 117270"},"PeriodicalIF":2.6,"publicationDate":"2025-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886355","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}

引用次数: 0

Contract design under an enhanced dynamic contagious process 增强动态传染过程下的契约设计

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-12-21 DOI: 10.1016/j.cam.2025.117266

Pengcheng Zhang , Jiannan Zhang , Guo Liu , Jingchao Li

In this paper, we discuss an optimal reinsurance contract design under continuous-time contagious insurance markets. The arrival of claims is modelled using an enhanced dynamic contagious process, which generalises the external-exciting Cox process with shot noise and the self-exciting Hawkes process. Additionally, the interdependencies between the self-exciting effect and the claim sizes are captured through a joint distribution. We derive closed-form expressions for insurance premiums under two pricing principles. A principal-agent problem is formulated to determine the optimal reinsurance contract, where the reinsurer chooses the premium level and corresponding compensation for claims. The insurer enters the contract if and only if the expected utility of its operating profit over the reinsurance term exceeds that of operating without reinsurance. Using the Lagrangian method, we obtain semi-closed-form solutions for the optimal reinsurance premium and compensation functions. To support our quantitative analysis, we provide several numerical examples that illustrate how key parameters and the dependency structure influence the optimal reinsurance controls.

本文讨论了连续时间传染保险市场下的最优再保险合同设计问题。索赔的到达使用增强的动态传染过程建模，该过程推广了带有小噪声的外部激励Cox过程和自激励Hawkes过程。此外，自激效应和索赔规模之间的相互依赖关系通过联合分布得到。我们在两种定价原则下推导出保险费的封闭形式表达式。利用委托代理问题确定最优再保险合同，再保险人选择保费水平和相应的赔付金额。当且仅当保险人在再保险期限内经营利润的预期效用超过无再保险经营的预期效用时，保险人签订合同。利用拉格朗日方法，得到了最优再保险保费和赔付函数的半封闭解。为了支持我们的定量分析，我们提供了几个数值例子来说明关键参数和依赖结构如何影响最优再保险控制。

{"title":"Contract design under an enhanced dynamic contagious process","authors":"Pengcheng Zhang , Jiannan Zhang , Guo Liu , Jingchao Li","doi":"10.1016/j.cam.2025.117266","DOIUrl":"10.1016/j.cam.2025.117266","url":null,"abstract":"<div><div>In this paper, we discuss an optimal reinsurance contract design under continuous-time contagious insurance markets. The arrival of claims is modelled using an enhanced dynamic contagious process, which generalises the external-exciting Cox process with shot noise and the self-exciting Hawkes process. Additionally, the interdependencies between the self-exciting effect and the claim sizes are captured through a joint distribution. We derive closed-form expressions for insurance premiums under two pricing principles. A principal-agent problem is formulated to determine the optimal reinsurance contract, where the reinsurer chooses the premium level and corresponding compensation for claims. The insurer enters the contract if and only if the expected utility of its operating profit over the reinsurance term exceeds that of operating without reinsurance. Using the Lagrangian method, we obtain semi-closed-form solutions for the optimal reinsurance premium and compensation functions. To support our quantitative analysis, we provide several numerical examples that illustrate how key parameters and the dependency structure influence the optimal reinsurance controls.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"481 ","pages":"Article 117266"},"PeriodicalIF":2.6,"publicationDate":"2025-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145842394","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}

引用次数: 0

Confounding properties of third-order component effects in three-level regular designs 三能级规则设计中三阶分量效应的混杂特性

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-12-20 DOI: 10.1016/j.cam.2025.117262

Chongya Yan, Zhi Li, Zhiming Li

For the three-level regular design, the aliased component-effect number pattern (ACNP) is crucial for describing the confounding information among all component effects. Most literature has primarily concentrated on the confounding relationship between main effects and two-factor interactions, assuming that all third- or higher-order components are negligible. However, when this assumption is inappropriate, it becomes essential to further study the confounding information among third-order component effects. This paper presents a method for analyzing the confounding of third-order component effects in the ACNP. For any three-level design D, we obtain the formulas of third-order confounding information according to three consulting sets: (i) H_qD, (ii) F_qqD, and (iii) DS_qr, where H_q is a three-level saturated design,

F_{q q} = H_{q} ∖ H_{q - 1}

and

S_{q r} = H_{q} ∖ H_{r} (r < q)

. Some examples are given to illustrate applications of the theoretical results.

对于三层规则设计，混叠分量效应数模式（ACNP）是描述各分量效应间混杂信息的关键。大多数文献主要集中在主效应和双因素相互作用之间的混淆关系，假设所有三阶或高阶成分可以忽略不计。然而，当这种假设不合适时，有必要进一步研究三阶分量效应之间的混杂信息。本文提出了一种分析ACNP中三阶分量效应混杂的方法。对于任意三能级设计D，我们根据三个咨询集(i) HqD, (ii) FqqD, (iii) DSqr得到三阶混杂信息的公式，其中Hq是一个三能级饱和设计，Fqq=Hq × Hq−1,Sqr=Hq × Hr（r<q）。给出了一些例子来说明理论结果的应用。

{"title":"Confounding properties of third-order component effects in three-level regular designs","authors":"Chongya Yan, Zhi Li, Zhiming Li","doi":"10.1016/j.cam.2025.117262","DOIUrl":"10.1016/j.cam.2025.117262","url":null,"abstract":"<div><div>For the three-level regular design, the aliased component-effect number pattern (ACNP) is crucial for describing the confounding information among all component effects. Most literature has primarily concentrated on the confounding relationship between main effects and two-factor interactions, assuming that all third- or higher-order components are negligible. However, when this assumption is inappropriate, it becomes essential to further study the confounding information among third-order component effects. This paper presents a method for analyzing the confounding of third-order component effects in the ACNP. For any three-level design <em>D</em>, we obtain the formulas of third-order confounding information according to three consulting sets: (i) <em>H<sub>q</sub></em><em>D</em>, (ii) <em>F<sub>qq</sub></em><em>D</em>, and (iii) <em>D</em><em>S<sub>qr</sub></em>, where <em>H<sub>q</sub></em> is a three-level saturated design, <span><math><mrow><msub><mi>F</mi><mrow><mi>q</mi><mi>q</mi></mrow></msub><mo>=</mo><msub><mi>H</mi><mi>q</mi></msub><mrow><mo>∖</mo></mrow><msub><mi>H</mi><mrow><mi>q</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></math></span> and <span><math><mrow><msub><mi>S</mi><mrow><mi>q</mi><mi>r</mi></mrow></msub><mo>=</mo><msub><mi>H</mi><mi>q</mi></msub><mrow><mo>∖</mo></mrow><msub><mi>H</mi><mi>r</mi></msub><mrow><mo>(</mo><mi>r</mi><mo><</mo><mi>q</mi><mo>)</mo></mrow></mrow></math></span>. Some examples are given to illustrate applications of the theoretical results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"480 ","pages":"Article 117262"},"PeriodicalIF":2.6,"publicationDate":"2025-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145842204","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}

引用次数: 0

Second-order one-parameter maximum-principle-preserving and energy stable difference scheme for the Allen-Cahn equation Allen-Cahn方程的二阶单参数最大保原理和能量稳定差分格式

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-12-20 DOI: 10.1016/j.cam.2025.117276

Hao Han , Zengqiang Tan , Xiaoqiang Yan

This paper presents a novel second-order one-parameter linearized finite difference scheme for solving the Allen-Cahn equation with the periodic boundary condition, which is derived by combining the central difference approximation in space and the one-parameter method with an extrapolation in time. It is shown that the derived fully discrete schemes are uniquely solvable and able to preserve the discrete maximum principle and energy stability under appropriate conditions. Moreover, the maximum-norm error estimate of the schemes are studied and the scheme can arrive at second-order accuracy both in time and space. Several numerical examples are conducted to validate the theoretical results.

本文将空间上的中心差分近似与时间上的单参数外推法相结合，导出了求解具有周期边界条件的Allen-Cahn方程的一种新的二阶单参数线性化有限差分格式。结果表明，所导出的全离散格式是唯一可解的，并且在适当条件下能够保持离散极大值原理和能量稳定性。此外，研究了方案的最大范数误差估计，该方案在时间和空间上都能达到二阶精度。通过数值算例验证了理论结果。

引用次数: 0

Nested-conditional factorization approach to Asian options pricing 亚洲期权定价的嵌套条件分解方法

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-12-19 DOI: 10.1016/j.cam.2025.117264

Riccardo Brignone

In this paper, we propose a new approach to Asian options pricing under the Black-Scholes model that is based on the observation that, if the asset price follows a geometric Brownian motion, then the Laplace transform of the reciprocal of the arithmetic average of the asset price conditional on the price level at the endpoints of the given time period is known fully explicitly. Based on this, we propose two new option pricing formulas. In the first, we approximate the conditional distribution of the reciprocal of the arithmetic average with a gamma random variable and develop a fast and accurate approximating formula for Asian option prices. In the second, we develop a semi-analytical option pricing formula based on the numerical inversion of the aforementioned conditional Laplace transform, which provides an efficient and extremely accurate solution for the price of a large class of Asian-style derivatives, such as floating-strike Asian options and Australian options. Finally, we show how the proposed pricing approach can be applied to more complex models than Black-Scholes.

本文提出了一种基于Black-Scholes模型的亚洲期权定价新方法，该方法基于以下观察：如果资产价格遵循几何布朗运动，则在给定时间段端点价格水平的条件下，资产价格的算术平均值的倒数的拉普拉斯变换是完全明确已知的。在此基础上，我们提出了两个新的期权定价公式。本文首先用gamma随机变量近似算术平均倒数的条件分布，并推导出亚洲期权价格快速准确的近似公式。其次，我们基于上述条件拉普拉斯变换的数值反演，建立了一个半解析式期权定价公式，该公式为亚洲期权和澳大利亚期权等一类亚洲式衍生品的价格提供了一个高效且极其准确的解。最后，我们展示了所提出的定价方法如何应用于比Black-Scholes更复杂的模型。

引用次数: 0

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Journal of Computational and Applied Mathematics

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀