Applied Numerical Mathematics最新文献_第3页

Parametric finite element method for a nonlocal curvature flow

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-10 DOI: 10.1016/j.apnum.2025.02.003

Jie Li, Lifang Pei

引用次数: 0

Finite element error estimation for parabolic optimal control problems with time delay

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-05 DOI: 10.1016/j.apnum.2025.02.002

Xindan Zhang , Jianping Zhao , Yanren Hou

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Orthogonal wavelet method for multi-stage expansion and contraction options under stochastic volatility

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-05 DOI: 10.1016/j.apnum.2025.02.001

Dana Černá

{"title":"Orthogonal wavelet method for multi-stage expansion and contraction options under stochastic volatility","authors":"Dana Černá","doi":"10.1016/j.apnum.2025.02.001","DOIUrl":"10.1016/j.apnum.2025.02.001","url":null,"abstract":"<div><div>Multi-stage expansion and contraction options are real options enabling an investment project to be scaled up or down in response to market conditions at predetermined future dates. We examine an investment project focused on producing a specific commodity, with the project value dependent on the market price of this commodity. We then study the value of options to either increase or decrease production at specific future dates based on predetermined factors and costs. Under the assumption that the commodity price follows a geometric Brownian motion and the volatility is stochastic, multiple partial differential equations represent the valuation model for these options. This paper aims to establish two new pricing models for multi-stage expansion and contraction options: one where variance follows a geometric Brownian motion and another governed by the Cox–Ingersoll–Ross process. Another aim is to propose and analyze an efficient wavelet-based numerical method for these models. The method employs the Galerkin method with a recently constructed orthogonal cubic spline wavelet basis and the Crank-Nicolson scheme enhanced by Richardson extrapolation. We establish the existence and uniqueness of the solution, provide error estimates for the proposed method, and derive bounds for condition numbers of the resulting matrices arising from discretization. The method is applied to options related to iron-ore mining investment projects to verify the relevance of the method and show its benefits, which are a high-order convergence rate, well-conditioned discretization matrices, and an efficient solution of the resulting system of equations using a small number of iterations.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"212 ","pages":"Pages 155-175"},"PeriodicalIF":2.2,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143377000","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

Finite element analysis for the Navier-Lamé eigenvalue problem

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.09.023

Felipe Lepe , Gonzalo Rivera , Jesus Vellojin

引用次数: 0

A hybrid interpolating element-free Galerkin method for 3D steady-state convection diffusion problems

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.09.024

Yujun Cheng , Miaojuan Peng , Yumin Cheng

{"title":"A hybrid interpolating element-free Galerkin method for 3D steady-state convection diffusion problems","authors":"Yujun Cheng , Miaojuan Peng , Yumin Cheng","doi":"10.1016/j.apnum.2024.09.024","DOIUrl":"10.1016/j.apnum.2024.09.024","url":null,"abstract":"<div><div>This study investigates a hybrid interpolating element-free Galerkin (HIEFG) method for solving 3D convection diffusion problems. The HIEFG approach divides a 3D solution domain into a sequence of interconnected 2D sub-domains, and in these 2D sub-domains, the interpolating element-free Galerkin (IEFG) method is applied to form the discretized equations. The improved interpolating moving least-squares (IMLS) method is used to obtain the shape function of the IEFG method for 2D problems. The finite difference method is employed to combine the discretized equations in 2D sub-domains in the splitting direction. Then, the HIEFG method's formulas are derived for steady-state convection diffusion problems in 3D solution domain. Three numerical examples are used to discuss the impacts of the number of nodes, the number of split layers, and the scaling parameters of the influence domain on the computational precision and CPU time of the HIEFG technique. Imposing boundary conditions directly and the dimension splitting technique in this method significantly improves the computational speed greatly.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 21-37"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143097175","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

Efficient estimates for matrix-inverse quadratic forms 矩阵反二次型的有效估计值

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.01.013

Emmanouil Bizas , Marilena Mitrouli , Ondřej Turek

引用次数: 0

A new fast algorithm for computing the mock-Chebyshev nodes 计算模拟切比雪夫节点的新型快速算法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.03.002

B. Ali Ibrahimoglu

{"title":"A new fast algorithm for computing the mock-Chebyshev nodes","authors":"B. Ali Ibrahimoglu","doi":"10.1016/j.apnum.2024.03.002","DOIUrl":"10.1016/j.apnum.2024.03.002","url":null,"abstract":"<div><div>Interpolation by polynomials on equispaced points is not always convergent due to the Runge phenomenon, and also, the interpolation process is exponentially ill-conditioned. By taking advantage of the optimality of the interpolation processes on the Chebyshev-Lobatto nodes, one of the best strategies to defeat the Runge phenomenon is to use the mock-Chebyshev nodes for polynomial interpolation. Mock-Chebyshev nodes asymptotically follow the Chebyshev distribution, and they are selected from a sufficiently large set of equispaced nodes. However, there are few studies in the literature regarding the computation of these points.</div><div>In a recent paper <span><span>[1]</span></span>, we have introduced a fast algorithm for computing the mock-Chebyshev nodes for a given set of <span><math><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span> Chebyshev-Lobatto points using the distance between each pair of consecutive points. In this study, we propose a modification of the algorithm by changing the function to compute the quotient of the distance and show that this modified algorithm is also fast and stable; and gives a more accurate grid satisfying the conditions of a mock-Chebyshev grid with the complexity being <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span><span>. Some numerical experiments using the points obtained by this modified algorithm are given to show its effectiveness and numerical results are also provided. A bivariate generalization of the mock-Chebyshev nodes to the Padua interpolation points is discussed.</span></div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 246-255"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125652","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

Special Volume on Numerical Analysis and Scientific Computation with Applications

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.10.019

Dr Khalide Jbilou

引用次数: 0

Non trivial solutions for a system of coupled Ginzburg-Landau equations

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.10.010

Mariano De Leo , Juan Pablo Borgna , Cristian Huenchul

{"title":"Non trivial solutions for a system of coupled Ginzburg-Landau equations","authors":"Mariano De Leo , Juan Pablo Borgna , Cristian Huenchul","doi":"10.1016/j.apnum.2024.10.010","DOIUrl":"10.1016/j.apnum.2024.10.010","url":null,"abstract":"<div><div>This article addresses both the existence and properties of non-trivial solutions for a system of coupled Ginzburg-Landau equations derived from nematic-superconducting models. Its main goal is to provide a thorough numerical description of the region in the parameter space containing solutions that behave as a mixed (non trivial) nematic-superconducting state along with a rigorous proof for the existence of this region. More precisely, the rigorous approach establishes that the parameter space is divided into two regions with qualitatively different properties, according to the magnitude of the coupling constant: for small values (weak coupling), there is a unique non-trivial solution, and for large values (strong coupling), only trivial solutions exist. In addition, using a shooting method-based numerical approach, the profiles for the nematic and superconducting components of the non trivial solution are given, together with an algorithm computing the transition values representing the boundaries for the weak coupling region: from superconducting to mixed, and from mixed to nematic. Finally, numerical evidence is given for the existence of a third region, related to neither a small nor a strong coupling parameter (medium coupling) for which multiple non trivial solutions exist.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 271-289"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143141234","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 mathematical model for studying the Red Blood Cell magnetic susceptibility 研究红血球磁感应强度的数学模型

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.05.014

Protopapas Eleftherios , Vafeas Panayiotis , Hadjinicolaou Maria

{"title":"A mathematical model for studying the Red Blood Cell magnetic susceptibility","authors":"Protopapas Eleftherios , Vafeas Panayiotis , Hadjinicolaou Maria","doi":"10.1016/j.apnum.2024.05.014","DOIUrl":"10.1016/j.apnum.2024.05.014","url":null,"abstract":"<div><div><span><span>The susceptibility of the human Red Blood Cells (RBCs) under the action of magnetic fields, either serves as a biomarker in medical tests, e.g.. Magnetic Resonance Imaging, Nuclear Magnetic Resonance, </span>Magnetoencephalography, or it is used in diagnostic and therapeutical processes, e.g.. magnetophoresis for cell sorting. In the present manuscript we provide analytical expressions for the magnetic potential and the magnetic field </span>strength vector, when a magnetic field is applied to a RBC, modeled as a two-layered inverted spheroid. We introduce this way in the model the biconcave shape of the RBC and its structure (membrane and cytocol) in a more realistic representation, as until now, the RBC's shape was considered either as a sphere or a spheroid. The solution inside the RBC is obtained in R-separable form in terms of Legendre functions of the first and of the second kind and cyclic trigonometric functions, by applying appropriate boundary conditions on each layer. Our results reveal a non-uniform magnetic field inside the RBC. Parametric study of the solution, for various values of the physical properties of the RBC, is also provided, demonstrating the diamagnetic or the paramagnetic property of the RBC, which is strongly related to the health condition of the blood. The obtained solution may also serve for the justification of experimental results.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 356-365"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141138058","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