Applied Mathematics Letters最新文献

{"title":"Leighton–Wintner-type oscillation theorem for the discrete [formula omitted]-Laplacian","authors":"Kōdai Fujimoto, Kazuki Ishibashi, Masakazu Onitsuka","doi":"10.1016/j.aml.2025.109465","DOIUrl":"https://doi.org/10.1016/j.aml.2025.109465","url":null,"abstract":"This paper addresses oscillation problems for difference equations with a discrete <mml:math altimg=\"si3.svg\" display=\"inline\"><mml:mrow><mml:mi>p</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>-Laplacian. In general, applying the Riccati technique to discrete oscillations is difficult. However, this study established a Leighton–Wintner-type oscillation theorem using the Riccati technique. Three examples are provided to illustrate the results. In particular, we examined the oscillatory problem for a certain nonlinear difference equation, including the Harper model, and demonstrated that the solutions are oscillatory even when <mml:math altimg=\"si3.svg\" display=\"inline\"><mml:mrow><mml:mi>p</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> diverges to infinity.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"15 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990380","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}

{"title":"On the relation between the exponential of real matrices and that of dual matrices","authors":"Chengdong Liu, Yimin Wei, Pengpeng Xie","doi":"10.1016/j.aml.2025.109466","DOIUrl":"https://doi.org/10.1016/j.aml.2025.109466","url":null,"abstract":"Dual number matrices play a significant role in engineering applications such as kinematics and dynamics. The matrix exponential is ubiquitous in screw-based kinematics. In this paper, we develop an explicit formula for the dual matrix exponential. The result is closely related to the Fréchet derivative, which can be formed by the standard part and dual part of the original matrix. We only need to compute the exponential of a real matrix. Then, we give a formula of computing the dual quaternion matrix exponential. Our results are illustrated through a practical example from robotic kinematics.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"23 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990379","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}

{"title":"Geometric programming for multilinear systems with nonsingular [formula omitted]-tensors","authors":"Haibin Chen, Guanglu Zhou, Hong Yan","doi":"10.1016/j.aml.2025.109462","DOIUrl":"https://doi.org/10.1016/j.aml.2025.109462","url":null,"abstract":"We consider multilinear systems which arise in various applications, such as data mining and numerical differential equations. In this paper, we show that the multilinear system with a nonsingular <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mi mathvariant=\"script\">M</mml:mi></mml:math>-tensor can be formulated equivalently into a geometric programming (GP) problem which can be solved by the barrier-based interior point method with a worst-case polynomial-time complexity. To the best of our knowledge, there is not a complexity analysis for the existing algorithms of the multilinear systems. Numerical results are reported to show the efficiency of the proposed GP method.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"122 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990387","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}

{"title":"Optimal decay rate to the contact discontinuity for Navier–Stokes equations under generic perturbations","authors":"Lingjun Liu, Guiqin Qiu, Shu Wang, Lingda Xu","doi":"10.1016/j.aml.2025.109461","DOIUrl":"https://doi.org/10.1016/j.aml.2025.109461","url":null,"abstract":"This paper investigates the large-time asymptotic behavior of contact waves in 1-D compressible Navier–Stokes equations. We derive the optimal decay rate for generic initial perturbations, meaning the perturbation’s integral does not need to be zero. It is well-known that generic perturbations in Navier–Stokes equations generate diffusion waves, implying that the optimal decay rate for contact waves in the <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msup></mml:math>-norm is <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>. However, the presence of diffusion waves introduces error terms, leading to energy growth in the anti-derivatives of the perturbations. Furthermore, studying contact waves depends on certain structural conditions, which hold for the original system but not for its derivative systems. This makes it challenging to obtain accurate estimates for the energy of the derivatives.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"22 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990414","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}

{"title":"Stability analysis of a conservative reaction–diffusion system with rate controls","authors":"Jie Ding, Fei Xu, Zhi Ling","doi":"10.1016/j.aml.2025.109457","DOIUrl":"https://doi.org/10.1016/j.aml.2025.109457","url":null,"abstract":"This paper demonstrates the fundamental properties of a conservative reaction–diffusion system. The solution of the system exists globally and is unique, as well as uniformly converges to its constant equilibrium as time tends to infinity. In addition, the steady-state system only has a constant solution under a mass conservation condition.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"5 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990279","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}

{"title":"[formula omitted] estimates for fully nonlinear parabolic inequalities on [formula omitted] domains","authors":"Xuemei Li","doi":"10.1016/j.aml.2025.109459","DOIUrl":"https://doi.org/10.1016/j.aml.2025.109459","url":null,"abstract":"In this paper, we study boundary <mml:math altimg=\"si4.svg\" display=\"inline\"><mml:msup><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mi>δ</mml:mi></mml:mrow></mml:msup></mml:math> estimates for solution sets of fully nonlinear parabolic inequalities <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mrow><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">−</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"script\">M</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>u</mml:mi><mml:mo>,</mml:mo><mml:mi>λ</mml:mi><mml:mo>,</mml:mo><mml:mi>Λ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">≤</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">≤</mml:mo><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">−</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"script\">M</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>u</mml:mi><mml:mo>,</mml:mo><mml:mi>λ</mml:mi><mml:mo>,</mml:mo><mml:mi>Λ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> on <mml:math altimg=\"si5.svg\" display=\"inline\"><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>α</mml:mi></mml:mrow></mml:msup></mml:math> domains, which generalize results for elliptic equations in Li and Li (2023).","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"23 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990371","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}

{"title":"Energy-equidistributed moving mesh strategies for simulating Hamiltonian partial differential equations","authors":"Qinjiao Gao, Zhengjie Sun, Zongmin Wu","doi":"10.1016/j.aml.2025.109460","DOIUrl":"https://doi.org/10.1016/j.aml.2025.109460","url":null,"abstract":"This paper presents an innovative energy-equidistributed moving mesh strategy for simulating Hamiltonian partial differential equations (PDEs) characterized by solitons and rapid temporal variations. A novel framework, named the Energy Equidistribution Principles (EEPs), is introduced, highlighting the critical role of energy conservation in achieving accurate simulations. Building on EEPs, three kinds of energy-equidistributed moving mesh PDEs (EMMPDEs) are proposed, each grounded in different methodologies. These strategies are rigorously examined in terms of their convergence conditions and rates. Both theoretical analysis and numerical experiments demonstrate that the proposed EMMPDEs offer superior robustness and effectiveness in long-term simulations, compared to traditional arc-length-equidistributed MMPDEs.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"66 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990370","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}

{"title":"A novel time-domain SCT-BEM for transient heat conduction analysis","authors":"Xiaotong Gao, Yan Gu, Bo Yu","doi":"10.1016/j.aml.2025.109463","DOIUrl":"https://doi.org/10.1016/j.aml.2025.109463","url":null,"abstract":"Accurate and efficient treatment of domain integrals is critical for obtaining reliable and precise boundary element method (BEM) solutions in dynamic or time-dependent problems. Despite the success of existing techniques for handling domain integrals, significant challenges still remain, especially in time-dependent BEM analyses where time-dependent fundamental solutions often result in integrands with oscillations or near-singularities, particularly when small time steps are used. To address these issues, this study introduces an improved scaled coordinate transformation BEM (SCT-BEM), combined with a non-linear coordinate transformation, to enhance the robustness of domain integral evaluations in transient time-domain BEM. The proposed method is straightforward to implement, requiring minimal modifications to existing BEM frameworks, and significantly improves both the robustness and accuracy of domain integral evaluations in transient time-domain BEM.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"44 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990372","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}

{"title":"Propagation direction of traveling waves for a class of nonlocal dispersal bistable epidemic models","authors":"Yu-Xia Hao, Guo-Bao Zhang","doi":"10.1016/j.aml.2025.109458","DOIUrl":"https://doi.org/10.1016/j.aml.2025.109458","url":null,"abstract":"This work is devoted to studying the propagation direction of the following nonlocal dispersal epidemic model &lt;ce:display&gt;&lt;ce:formula&gt;&lt;ce:label&gt;(0.1)&lt;/ce:label&gt;&lt;mml:math altimg=\"si1.svg\" display=\"block\"&gt;&lt;mml:mfenced close=\"\" open=\"{\"&gt;&lt;mml:mrow&gt;&lt;mml:mtable align=\"axis\" columnlines=\"none none none none none none none none\" columnspacing=\"0.27em\" equalcolumns=\"false\" equalrows=\"false\"&gt;&lt;mml:mtr&gt;&lt;mml:mtd columnalign=\"right\"&gt;&lt;mml:mfrac&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;∂&lt;/mml:mi&gt;&lt;mml:mi&gt;u&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;∂&lt;/mml:mi&gt;&lt;mml:mi&gt;t&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:mfrac&gt;&lt;/mml:mtd&gt;&lt;mml:mtd columnalign=\"left\"&gt;&lt;mml:mo&gt;=&lt;/mml:mo&gt;&lt;mml:msub&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;d&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mn&gt;1&lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;/mml:msub&gt;&lt;mml:mfenced close=\")\" open=\"(\"&gt;&lt;mml:mrow&gt;&lt;mml:msub&gt;&lt;mml:mrow&gt;&lt;mml:mo linebreak=\"badbreak\"&gt;∫&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mi mathvariant=\"double-struck\"&gt;R&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:msub&gt;&lt;mml:mi&gt;J&lt;/mml:mi&gt;&lt;mml:mrow&gt;&lt;mml:mo&gt;(&lt;/mml:mo&gt;&lt;mml:mi&gt;y&lt;/mml:mi&gt;&lt;mml:mo&gt;−&lt;/mml:mo&gt;&lt;mml:mi&gt;x&lt;/mml:mi&gt;&lt;mml:mo&gt;)&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:mi&gt;u&lt;/mml:mi&gt;&lt;mml:mrow&gt;&lt;mml:mo&gt;(&lt;/mml:mo&gt;&lt;mml:mi&gt;y&lt;/mml:mi&gt;&lt;mml:mo&gt;,&lt;/mml:mo&gt;&lt;mml:mi&gt;t&lt;/mml:mi&gt;&lt;mml:mo&gt;)&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:mi&gt;d&lt;/mml:mi&gt;&lt;mml:mi&gt;y&lt;/mml:mi&gt;&lt;mml:mo&gt;−&lt;/mml:mo&gt;&lt;mml:mi&gt;u&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:mfenced&gt;&lt;mml:mo&gt;−&lt;/mml:mo&gt;&lt;mml:mi&gt;u&lt;/mml:mi&gt;&lt;mml:mo&gt;+&lt;/mml:mo&gt;&lt;mml:mi&gt;α&lt;/mml:mi&gt;&lt;mml:mi&gt;v&lt;/mml:mi&gt;&lt;mml:mo&gt;,&lt;/mml:mo&gt;&lt;mml:mspace width=\"1em\"&gt;&lt;/mml:mspace&gt;&lt;mml:mspace width=\"0.2777em\"&gt;&lt;/mml:mspace&gt;&lt;mml:mspace width=\"0.2777em\"&gt;&lt;/mml:mspace&gt;&lt;mml:mspace width=\"2em\"&gt;&lt;/mml:mspace&gt;&lt;mml:mspace width=\"1em\"&gt;&lt;/mml:mspace&gt;&lt;mml:mspace width=\"0.16667em\"&gt;&lt;/mml:mspace&gt;&lt;/mml:mtd&gt;&lt;mml:mtd columnalign=\"right\"&gt;&lt;/mml:mtd&gt;&lt;mml:mtd columnalign=\"left\"&gt;&lt;mml:mi&gt;x&lt;/mml:mi&gt;&lt;mml:mo&gt;∈&lt;/mml:mo&gt;&lt;mml:mi mathvariant=\"double-struck\"&gt;R&lt;/mml:mi&gt;&lt;mml:mo&gt;,&lt;/mml:mo&gt;&lt;mml:mspace width=\"1em\"&gt;&lt;/mml:mspace&gt;&lt;mml:mi&gt;t&lt;/mml:mi&gt;&lt;mml:mo&gt;&gt;&lt;/mml:mo&gt;&lt;mml:mn&gt;0&lt;/mml:mn&gt;&lt;mml:mo&gt;,&lt;/mml:mo&gt;&lt;/mml:mtd&gt;&lt;/mml:mtr&gt;&lt;mml:mtr&gt;&lt;mml:mtd columnalign=\"right\"&gt;&lt;mml:mfrac&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;∂&lt;/mml:mi&gt;&lt;mml:mi&gt;v&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;∂&lt;/mml:mi&gt;&lt;mml:mi&gt;t&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:mfrac&gt;&lt;/mml:mtd&gt;&lt;mml:mtd columnalign=\"left\"&gt;&lt;mml:mo&gt;=&lt;/mml:mo&gt;&lt;mml:msub&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;d&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mn&gt;2&lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;/mml:msub&gt;&lt;mml:mfenced close=\")\" open=\"(\"&gt;&lt;mml:mrow&gt;&lt;mml:msub&gt;&lt;mml:mrow&gt;&lt;mml:mo linebreak=\"badbreak\"&gt;∫&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mi mathvariant=\"double-struck\"&gt;R&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:msub&gt;&lt;mml:mi&gt;J&lt;/mml:mi&gt;&lt;mml:mrow&gt;&lt;mml:mo&gt;(&lt;/mml:mo&gt;&lt;mml:mi&gt;y&lt;/mml:mi&gt;&lt;mml:mo&gt;−&lt;/mml:mo&gt;&lt;mml:mi&gt;x&lt;/mml:mi&gt;&lt;mml:mo&gt;)&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:mi&gt;v&lt;/mml:mi&gt;&lt;mml:mrow&gt;&lt;mml:mo&gt;(&lt;/mml:mo&gt;&lt;mml:mi&gt;y&lt;/mml:mi&gt;&lt;mml:mo&gt;,&lt;/mml:mo&gt;&lt;mml:mi&gt;t&lt;/mml:mi&gt;&lt;mml:mo&gt;)&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:mi&gt;d&lt;/mml:mi&gt;&lt;mml:mi&gt;y&lt;/mml:mi&gt;&lt;mml:mo&gt;−&lt;/mml:mo&gt;&lt;mml:mi&gt;v&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:mfenced&gt;&lt;mml:mo&gt;−&lt;/mml:mo&gt;&lt;mml:mi&gt;β&lt;/mml:mi&gt;&lt;mml:mi&gt;v&lt;/mml:mi&gt;&lt;mml:mo&gt;+&lt;/mml:mo&gt;&lt;mml:mi&gt;g&lt;/mml:mi&gt;&lt;mml:mrow&gt;&lt;mml:mo&gt;(&lt;/mml:mo&gt;&lt;mml:mi&gt;u&lt;/mml:mi&gt;&lt;mml:mo&gt;)&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:mo&gt;,&lt;/mml:mo&gt;&lt;mml:mspace width=\"0.16667e","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"24 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990373","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}

{"title":"A shape-parameterized RBF-partition of unity technique for PDEs","authors":"Roberto Cavoretto, Alessandra De Rossi, Adeeba Haider","doi":"10.1016/j.aml.2024.109453","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109453","url":null,"abstract":"In this paper, we study a direct discretization technique based on a radial basis function partition of unity (RBF-PU) method, which is built to numerically solve partial differential equations (PDEs). Unlike commonly used shape parameter free polyharmonic spline kernels, in this work we focus on local radial kernels depending on the shape parameter associated with the basis functions. The resulting scheme generally leads to more flexibility and accuracy, in particular when a polynomial term is added to the local RBF expansion. To emphasize the benefits deriving from use of the direct approach, we also compare it with the RBF finite difference (RBF-FD) method both in terms of computational efficiency and accuracy. Numerical results show the method performance by solving some elliptic PDE problems.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"9 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990374","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}