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A new amplification-fitting approach in Newton-Cotes rules to tackling the high-frequency IVPs 牛顿-科茨规则中一种新的放大拟合方法，用于解决高频 IVP 问题
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-08-30 DOI: 10.1016/j.apnum.2024.08.024
Hosein Saadat , Sanaz Hami Hassan Kiyadeh , Ali Safaie , Ramin Goudarzi Karim , Fayyaz Khodadosti
{"title":"A new amplification-fitting approach in Newton-Cotes rules to tackling the high-frequency IVPs","authors":"Hosein Saadat ,&nbsp;Sanaz Hami Hassan Kiyadeh ,&nbsp;Ali Safaie ,&nbsp;Ramin Goudarzi Karim ,&nbsp;Fayyaz Khodadosti","doi":"10.1016/j.apnum.2024.08.024","DOIUrl":"10.1016/j.apnum.2024.08.024","url":null,"abstract":"<div><p>In this paper, we will further strengthen the fitting technique of the well-known Newton-Cotes rules. First, we fit Boole's rule using the found amplification factor, and then we use it to numerically solve first-order differential equations with oscillating solutions. If the Hamiltonian energy of the system remains almost constant then we investigate whether the new amplification-fitted methods can be used as symplectic methods for numerical integration.</p><p>The obtained results show the high accuracy of the new amplification-fitting Boole's rule-based methods.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142137307","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
On Gabor frames generated by B-splines, totally positive functions, and Hermite functions 关于由 B-样条函数、全正函数和赫米特函数生成的 Gabor 框架
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-08-30 DOI: 10.1016/j.apnum.2024.08.021
Riya Ghosh, A. Antony Selvan
{"title":"On Gabor frames generated by B-splines, totally positive functions, and Hermite functions","authors":"Riya Ghosh,&nbsp;A. Antony Selvan","doi":"10.1016/j.apnum.2024.08.021","DOIUrl":"10.1016/j.apnum.2024.08.021","url":null,"abstract":"<div><p>The frame set of a window <span><math><mi>ϕ</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo></math></span> is the subset of all lattice parameters <span><math><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>)</mo><mo>∈</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow><mrow><mn>2</mn></mrow></msubsup></math></span> such that <span><math><mi>G</mi><mo>(</mo><mi>ϕ</mi><mo>,</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>)</mo><mo>=</mo><mo>{</mo><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn><mi>π</mi><mi>i</mi><mi>β</mi><mi>m</mi><mo>⋅</mo></mrow></msup><mi>ϕ</mi><mo>(</mo><mo>⋅</mo><mo>−</mo><mi>α</mi><mi>k</mi><mo>)</mo><mo>:</mo><mi>k</mi><mo>,</mo><mi>m</mi><mo>∈</mo><mi>Z</mi><mo>}</mo></math></span> forms a frame for <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo></math></span>. In this paper, we investigate the frame set of B-splines, totally positive functions, and Hermite functions. We derive a sufficient condition for Gabor frames using the connection between sampling theory in shift-invariant spaces and Gabor analysis. As a consequence, we obtain a new frame region belonging to the frame set of B-splines and Hermite functions. For a class of functions that includes certain totally positive functions, we prove that for any choice of lattice parameters <span><math><mi>α</mi><mo>,</mo><mi>β</mi><mo>&gt;</mo><mn>0</mn></math></span> with <span><math><mi>α</mi><mi>β</mi><mo>&lt;</mo><mn>1</mn></math></span>, there exists a <span><math><mi>γ</mi><mo>&gt;</mo><mn>0</mn></math></span> depending on <em>αβ</em> such that <span><math><mi>G</mi><mo>(</mo><mi>ϕ</mi><mo>(</mo><mi>γ</mi><mo>⋅</mo><mo>)</mo><mo>,</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>)</mo></math></span> forms a frame for <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo></math></span>. Our results give explicit frame bounds.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142137304","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 polynomial collocation method for a class of singular fractional differential equations 一类奇异分数微分方程的多项式配位法
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-08-28 DOI: 10.1016/j.apnum.2024.08.017
Ghulam Abbas Khan , Kaido Lätt , Magda Rebelo
{"title":"A polynomial collocation method for a class of singular fractional differential equations","authors":"Ghulam Abbas Khan ,&nbsp;Kaido Lätt ,&nbsp;Magda Rebelo","doi":"10.1016/j.apnum.2024.08.017","DOIUrl":"10.1016/j.apnum.2024.08.017","url":null,"abstract":"<div><p>In this work we consider a class of singular fractional differential equations (SFDEs). Using a suitable variable transformation we rewrite the SFDE as a cordial Volterra integral equation and propose a polynomial collocation method to find an approximate solution of the original problem. We provide the error analysis of the numerical method and we illustrate its feasibility and accuracy through some numerical examples.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142136427","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
Existence, uniqueness and Ulam–Hyers stability result for variable order fractional predator-prey system and it's numerical solution 变阶分数捕食者-猎物系统的存在性、唯一性和 Ulam-Hyers 稳定性结果及其数值解法
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-08-28 DOI: 10.1016/j.apnum.2024.08.019
Mohd Kashif, Manpal Singh
{"title":"Existence, uniqueness and Ulam–Hyers stability result for variable order fractional predator-prey system and it's numerical solution","authors":"Mohd Kashif,&nbsp;Manpal Singh","doi":"10.1016/j.apnum.2024.08.019","DOIUrl":"10.1016/j.apnum.2024.08.019","url":null,"abstract":"<div><p>This study presents an approximate numerical technique for solving time fractional advection-diffusion-reaction predator-prey equations with variable order (VO), where the analyzed fractional derivatives of VO are in the Caputo sense. Results for Ulam–Hyers stability are shown, as well as the existence and uniqueness of solutions. It is suggested to use a numerical approximation based on the shifted second kind of airfoil polynomials to solve the equations under consideration. A fractional derivative operational matrix with VO is derived for shifted airfoil polynomials, which will be used to compute the unknown function. The main equations are transformed into a set of algebraic equations by substituting the aforementioned operational matrix into the equations under consideration and utilizing the properties of the shifted airfoil polynomial along with the collocation points. A numerical solution is obtained by solving the acquired set of algebraic equations. To verify the accuracy and efficiency of the discussed scheme, several illustrative examples have been considered. The results obtained by the proposed method demonstrate the efficiency and superiority of the method compared to other existing methods.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142163200","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 finite volume method for a nonlocal thermistor problem 非局部热敏电阻问题的有限体积法
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-08-28 DOI: 10.1016/j.apnum.2024.08.016
Ibrahim Dahi , Moulay Rchid Sidi Ammi , Montasser Hichmani
{"title":"A finite volume method for a nonlocal thermistor problem","authors":"Ibrahim Dahi ,&nbsp;Moulay Rchid Sidi Ammi ,&nbsp;Montasser Hichmani","doi":"10.1016/j.apnum.2024.08.016","DOIUrl":"10.1016/j.apnum.2024.08.016","url":null,"abstract":"<div><p>In this work, we consider a more general version of the nonlocal thermistor problem, which describes the temperature diffusion produced when an electric current passes through a material. We investigate the doubly nonlinear problem where the nonlocal term is present on the right-hand side of the equation that describes the temperature evolution. Specifically, we employ topological degree theory to establish the existence of a solution to the considered problem. Furthermore, we separately address the uniqueness of the obtained solution. Additionally, we establish a priori estimates to demonstrate the convergence of a developed finite volume scheme used for the discretization of the continuous parabolic problem. Finally, to numerically simulate the proposed finite volume scheme, we use the Picard-type iteration process for the fully implicit scheme and approximate the nonlocal term represented by the integral with Simpson's rule to validate the efficiency and robustness of the proposed scheme.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142089347","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
Superconvergent method for weakly singular Fredholm-Hammerstein integral equations with non-smooth solutions and its application 具有非光滑解的弱奇异弗雷德霍姆-哈默斯坦积分方程的超融合方法及其应用
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-08-28 DOI: 10.1016/j.apnum.2024.08.018
Arnab Kayal, Moumita Mandal
{"title":"Superconvergent method for weakly singular Fredholm-Hammerstein integral equations with non-smooth solutions and its application","authors":"Arnab Kayal,&nbsp;Moumita Mandal","doi":"10.1016/j.apnum.2024.08.018","DOIUrl":"10.1016/j.apnum.2024.08.018","url":null,"abstract":"<div><p>In this article, we propose shifted Jacobi spectral Galerkin method (SJSGM) and iterated SJSGM to solve nonlinear Fredholm integral equations of Hammerstein type with weakly singular kernel. We have rigorously studied convergence analysis of the proposed methods. Even though the exact solution exhibits non-smooth behaviour, we manage to achieve superconvergence order for the iterated SJSGM. Further, using smoothing transformation, we improve the regularity of the exact solution, which enhances the convergence order of the SJSGM and iterated SJSGM. We have also shown the applicability of our proposed methods to high-order nonlinear weakly singular integro-differential equations and achieved superconvergence. Several numerical examples have been implemented to demonstrate the theoretical results.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142137305","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
Algebraic conditions for stability in Runge-Kutta methods and their certification via semidefinite programming Runge-Kutta 方法稳定性的代数条件及其通过半有限编程的认证
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-08-23 DOI: 10.1016/j.apnum.2024.08.015
Austin Juhl, David Shirokoff
{"title":"Algebraic conditions for stability in Runge-Kutta methods and their certification via semidefinite programming","authors":"Austin Juhl,&nbsp;David Shirokoff","doi":"10.1016/j.apnum.2024.08.015","DOIUrl":"10.1016/j.apnum.2024.08.015","url":null,"abstract":"<div><p>In this work, we present approaches to rigorously certify <em>A</em>- and <span><math><mi>A</mi><mo>(</mo><mi>α</mi><mo>)</mo></math></span>-stability in Runge-Kutta methods through the solution of convex feasibility problems defined by linear matrix inequalities. We adopt two approaches. The first is based on sum-of-squares programming applied to the Runge-Kutta <em>E</em>-polynomial and is applicable to both <em>A</em>- and <span><math><mi>A</mi><mo>(</mo><mi>α</mi><mo>)</mo></math></span>-stability. In the second, we sharpen the algebraic conditions for <em>A</em>-stability of Cooper, Scherer, Türke, and Wendler to incorporate the Runge-Kutta order conditions. We demonstrate how the theoretical improvement enables the practical use of these conditions for certification of <em>A</em>-stability within a computational framework. We then use both approaches to obtain rigorous certificates of stability for several diagonally implicit schemes devised in the literature.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142149995","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 macro BDM H-div mixed finite element on polygonal and polyhedral meshes 多边形和多面体网格上的宏 BDM H-div 混合有限元
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-08-22 DOI: 10.1016/j.apnum.2024.08.013
Xuejun Xu , Xiu Ye , Shangyou Zhang
{"title":"A macro BDM H-div mixed finite element on polygonal and polyhedral meshes","authors":"Xuejun Xu ,&nbsp;Xiu Ye ,&nbsp;Shangyou Zhang","doi":"10.1016/j.apnum.2024.08.013","DOIUrl":"10.1016/j.apnum.2024.08.013","url":null,"abstract":"<div><p>A BDM type of <span><math><mi>H</mi><mo>(</mo><mi>div</mi><mo>)</mo></math></span> mixed finite element is constructed on polygonal and polyhedral meshes. The flux space is the <span><math><mi>H</mi><mo>(</mo><mi>div</mi><mo>)</mo></math></span> subspace of the <em>n</em>-product <span><math><msub><mrow><mi>Π</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi></mrow></msub><msup><mrow><mo>(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>d</mi></mrow></msup></math></span> space such that the divergence is a one-piece <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub></math></span> polynomial on the big polygon or polyhedron <em>T</em>. Here we assume the 2D polygon can be subdivided into triangles by connecting only one vertex with some vertices of the polygon. For the 3D polyhedron we assume it can be subdivided into tetrahedra, with no added vertex on subdividing its face-polygons, and with either no internal edge or one internal edge. Such mixed finite elements can be more economic on quadrilateral and hexahedral meshes, compared with the standard BDM mixed element on triangular and tetrahedral meshes. Numerical tests and comparisons with the triangular and tetrahedral BDM finite elements are provided.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142049103","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
Progressive iterative Schoenberg-Marsden variation diminishing operator and related quadratures 渐进迭代勋伯格-马斯登变异递减算子及相关二次函数
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-08-22 DOI: 10.1016/j.apnum.2024.08.014
Elena Fornaca, Paola Lamberti
{"title":"Progressive iterative Schoenberg-Marsden variation diminishing operator and related quadratures","authors":"Elena Fornaca,&nbsp;Paola Lamberti","doi":"10.1016/j.apnum.2024.08.014","DOIUrl":"10.1016/j.apnum.2024.08.014","url":null,"abstract":"<div><p>In this paper we propose an approximation method based on the classical Schoenberg-Marsden variation diminishing operator with applications to the construction of new quadrature rules. We compare the new operator with the multilevel one studied in <span><span>[12]</span></span> in order to characterize both of them with respect to the well known classical one. We discuss convergence properties and present numerical experiments.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0168927424002101/pdfft?md5=6508653513a118f94937cbfd3c6e9f93&pid=1-s2.0-S0168927424002101-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142049105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Modified Neumann–Neumann methods for semi- and quasilinear elliptic equations 半线性和准线性椭圆方程的修正诺伊曼-诺伊曼方法
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-08-21 DOI: 10.1016/j.apnum.2024.08.011
Emil Engström, Eskil Hansen
{"title":"Modified Neumann–Neumann methods for semi- and quasilinear elliptic equations","authors":"Emil Engström,&nbsp;Eskil Hansen","doi":"10.1016/j.apnum.2024.08.011","DOIUrl":"10.1016/j.apnum.2024.08.011","url":null,"abstract":"<div><p>The Neumann–Neumann method is a commonly employed domain decomposition method for linear elliptic equations. However, the method exhibits slow convergence when applied to semilinear equations and does not seem to converge at all for certain quasilinear equations. We therefore propose two modified Neumann–Neumann methods that have better convergence properties and require fewer computations. We provide numerical results that show the advantages of these methods when applied to both semilinear and quasilinear equations. We also prove linear convergence with mesh-independent error reduction under certain assumptions on the equation. The analysis is carried out on general Lipschitz domains and relies on the theory of nonlinear Steklov–Poincaré operators.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0168927424002071/pdfft?md5=a635194882b5e6c159bfac4c6b2d40c5&pid=1-s2.0-S0168927424002071-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142089348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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