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De la Vallée Poussin filtered polynomial approximation on the half–line De la Vallée Poussin 半线多项式滤波近似法
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-09-16 DOI: 10.1016/j.apnum.2024.09.003
Donatella Occorsio , Woula Themistoclakis
{"title":"De la Vallée Poussin filtered polynomial approximation on the half–line","authors":"Donatella Occorsio ,&nbsp;Woula Themistoclakis","doi":"10.1016/j.apnum.2024.09.003","DOIUrl":"10.1016/j.apnum.2024.09.003","url":null,"abstract":"<div><div>On the half line, we introduce a new sequence of near-best uniform approximation polynomials, easily computable by the values of the approximated function at a truncated number of Laguerre zeros. Such approximation polynomials come from a discretization of filtered Fourier–Laguerre partial sums, which are filtered using a de la Vallée Poussin (VP) filter. They have the peculiarity of depending on two parameters: a truncation parameter that determines how many of the <em>n</em> Laguerre zeros are considered, and a localization parameter, which determines the range of action of the VP filter we will apply. As <span><math><mi>n</mi><mo>→</mo><mo>∞</mo></math></span>, under simple assumptions on such parameters and the Laguerre exponents of the involved weights, we prove that the new VP filtered approximation polynomials have uniformly bounded Lebesgue constants and uniformly convergence at a near–best approximation rate, for any locally continuous function on the semiaxis.</div><div>The numerical experiments have validated the theoretical results. In particular, they show a better performance of the proposed VP filtered approximation versus the truncated Lagrange interpolation at the same nodes, especially for functions a.e. very smooth with isolated singularities. In such cases, we see a more localized approximation and a satisfactory reduction of the Gibbs phenomenon.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421775","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
A novel least squares approach generating approximations orthogonal to the null space of the operator 一种新的最小二乘法，产生与算子空域正交的近似值
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-09-14 DOI: 10.1016/j.apnum.2024.09.015
Eunjung Lee, Youngmin Shin
{"title":"A novel least squares approach generating approximations orthogonal to the null space of the operator","authors":"Eunjung Lee,&nbsp;Youngmin Shin","doi":"10.1016/j.apnum.2024.09.015","DOIUrl":"10.1016/j.apnum.2024.09.015","url":null,"abstract":"<div><p>We introduce a novel least squares functional specifically formulated to solve linear partial differential equations with operators that have a nonempty null space. Our method involves projecting the solution onto the orthogonal complement of the operator's null space to overcome challenges encountered by conventional numerical methods when nonzero null components are present. We describe the theoretical framework of the proposed method and validate it through numerical examples that show improved accuracy and usability in cases where traditional methods are less effective due to significant null space components. Overall, this approach provides a practical and reliable solution for partial differential equations with substantial null space components.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142242982","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 comparative study on numerical methods for Fredholm integro-differential equations of convection-diffusion problem with integral boundary conditions 带积分边界条件的对流扩散问题弗雷德霍尔积分微分方程数值方法的比较研究
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-09-13 DOI: 10.1016/j.apnum.2024.09.001
Sekar Elango , L. Govindarao , R. Vadivel
{"title":"A comparative study on numerical methods for Fredholm integro-differential equations of convection-diffusion problem with integral boundary conditions","authors":"Sekar Elango ,&nbsp;L. Govindarao ,&nbsp;R. Vadivel","doi":"10.1016/j.apnum.2024.09.001","DOIUrl":"10.1016/j.apnum.2024.09.001","url":null,"abstract":"<div><p>This paper numerically solves Fredholm integro-differential equations with small parameters and integral boundary conditions. The solution of these equations has a boundary layer at the right boundary. A central difference scheme approximates the second-order derivative, a backward difference (upwind scheme) approximates the first-order derivative, and the trapezoidal rule is used for the integral term with a Shishkin mesh. It is shown that theoretically, the proposed scheme is uniformly convergent with almost first-order convergence. Further to improve the order of convergence from first order to second order, we use the post-processing and the hybrid scheme. Two numerical examples are computed to support the theoretical results.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142229354","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
Exact solution for a discrete-time SIR model 离散时间 SIR 模型的精确解
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-09-12 DOI: 10.1016/j.apnum.2024.09.014
Márcia Lemos-Silva , Sandra Vaz , Delfim F.M. Torres
{"title":"Exact solution for a discrete-time SIR model","authors":"Márcia Lemos-Silva ,&nbsp;Sandra Vaz ,&nbsp;Delfim F.M. Torres","doi":"10.1016/j.apnum.2024.09.014","DOIUrl":"10.1016/j.apnum.2024.09.014","url":null,"abstract":"<div><p>We propose a nonstandard finite difference scheme for the Susceptible–Infected–Removed (SIR) continuous model. We prove that our discretized system is dynamically consistent with its continuous counterpart and we derive its exact solution. We end with the analysis of the long-term behavior of susceptible, infected and removed individuals, illustrating our results with examples. In contrast with the SIR discrete-time model available in the literature, our new model is simultaneously mathematically and biologically sound.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0168927424002514/pdfft?md5=59d392bacfd7e04cd930aa9196f19ec9&pid=1-s2.0-S0168927424002514-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142229365","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
On differential equations with exponential nonlinearities 论指数非线性微分方程
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-09-12 DOI: 10.1016/j.apnum.2024.08.020
Armands Gritsans , Felix Sadyrbaev
{"title":"On differential equations with exponential nonlinearities","authors":"Armands Gritsans ,&nbsp;Felix Sadyrbaev","doi":"10.1016/j.apnum.2024.08.020","DOIUrl":"10.1016/j.apnum.2024.08.020","url":null,"abstract":"<div><div>Two-point boundary value problems for the second order nonlinear ordinary differential equations, arising in the heat conductivity theory, are considered. Multiplicity and existence results are established. The properties of solutions are studied. Estimates of the number of solutions are obtained. A bifurcation analysis was made and the bifurcation curves were presented. The analytical technique together with the phase plane analysis is used to obtain the results.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142358081","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 for a generalized form of nonlinear cordial Volterra integral equations using quasilinearization and Legendre-collocation methods 用准线性化和 Legendre-collocation 方法数值求解非线性 cordial Volterra 积分方程的广义形式
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-09-12 DOI: 10.1016/j.apnum.2024.09.013
Salwan Tareq Abdulghafoor, Esmaeil Najafi
{"title":"Numerical solution for a generalized form of nonlinear cordial Volterra integral equations using quasilinearization and Legendre-collocation methods","authors":"Salwan Tareq Abdulghafoor,&nbsp;Esmaeil Najafi","doi":"10.1016/j.apnum.2024.09.013","DOIUrl":"10.1016/j.apnum.2024.09.013","url":null,"abstract":"<div><p>In this article, we propose a numerical method for a general form of nonlinear cordial Volterra integral equations. We discuss conditions that under them the problem has solutions. Since the existence of solutions for the problem depends on the solvability of a scalar equation and also a linear form of the problem, then we employ quasilinearization technique in which solving a nonlinear problem is reduced to solve a sequence of linear equations. The existence of solutions of linear equations and their quadratically convergence to the solutions of the nonlinear problem is considered. For the numerical solution of the produced linear equations we apply Legendre-collocation method along with a regularization technique for the quadrature formulas. We discuss the error analysis of the collocation method considering that the cordial Volterra integral operators are noncompact. To test the efficiency and accuracy of the proposed method, the solution of different cases of numerical examples are reported.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142242882","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
Treatment of 3D diffusion problems with discontinuous coefficients and Dirac curvilinear sources 处理具有不连续系数和狄拉克曲线源的三维扩散问题
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-09-12 DOI: 10.1016/j.apnum.2024.09.012
E. Bejaoui, F. Ben Belgacem
{"title":"Treatment of 3D diffusion problems with discontinuous coefficients and Dirac curvilinear sources","authors":"E. Bejaoui,&nbsp;F. Ben Belgacem","doi":"10.1016/j.apnum.2024.09.012","DOIUrl":"10.1016/j.apnum.2024.09.012","url":null,"abstract":"<div><div>Three-dimensional diffusion problems with discontinuous coefficients and unidimensional Dirac sources arise in a number of fields. The statement we pursue is a singular-regular expansion where the singularity, capturing the stiff behavior of the potential, is expressed by a convolution formula using the Green kernel of the Laplace operator. The correction term, aimed at restoring the boundary conditions, fulfills a variational Poisson equation set in the Sobolev space <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>, which can be approximated using finite element methods. The mathematical justification of the proposed expansion is the main focus, particularly when the variable diffusion coefficients are continuous, or have jumps. A computational study concludes the paper with some numerical examples. The potential is approximated by a combined method: (singularity, by integral formulas, correction, by linear finite elements). The convergence is discussed to highlight the practical benefits brought by different expansions, for continuous and discontinuous coefficients.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142312992","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 fourth order Runge-Kutta type of exponential time differencing and triangular spectral element method for two dimensional nonlinear Maxwell's equations 针对二维非线性麦克斯韦方程的四阶 Runge-Kutta 指数时差和三角谱元法
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-09-11 DOI: 10.1016/j.apnum.2024.09.008
Wenting Shao , Cheng Chen
{"title":"A fourth order Runge-Kutta type of exponential time differencing and triangular spectral element method for two dimensional nonlinear Maxwell's equations","authors":"Wenting Shao ,&nbsp;Cheng Chen","doi":"10.1016/j.apnum.2024.09.008","DOIUrl":"10.1016/j.apnum.2024.09.008","url":null,"abstract":"<div><p>In this paper, we study a numerical scheme to solve the nonlinear Maxwell's equations. The discrete scheme is based on the triangular spectral element method (TSEM) in space and the exponential time differencing fourth-order Runge-Kutta (ETDRK4) method in time. TSEM has the advantages of spectral accuracy and geometric flexibility. The ETD method involves exact integration of the linear part of the governing equation followed by an approximation of an integral involving the nonlinear terms. The RK4 scheme is introduced for the time integration of the nonlinear terms. The stability region of the ETDRK4 method is depicted. Moreover, the contour integral in the complex plan is utilized and improved to compute the matrix function required by the implementation of ETDRK4. The numerical results demonstrate that our proposed method is of exponential convergence with the order of basis function in space and fourth order accuracy in time.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142242981","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 scheme for a system of green Fredholm integral equations 绿色弗雷德霍姆积分方程系统的超融合方案
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-09-11 DOI: 10.1016/j.apnum.2024.09.009
Rakesh Kumar, Kapil Kant, B.V. Rathish Kumar
{"title":"Superconvergent scheme for a system of green Fredholm integral equations","authors":"Rakesh Kumar,&nbsp;Kapil Kant,&nbsp;B.V. Rathish Kumar","doi":"10.1016/j.apnum.2024.09.009","DOIUrl":"10.1016/j.apnum.2024.09.009","url":null,"abstract":"<div><p>In this study, a numerical scheme to a system of second-kind linear Fredholm integral equations featuring a Green's kernel function is proposed. This involves introducing Galerkin and iterated Galerkin (IG) methods based on piecewise polynomials to tackle the integral model. A thorough analysis of convergence and error for these proposed methods is carried out. Firstly, the existence and uniqueness of solutions for the Galerkin and iterated Galerkin methods are established. Later, the order of convergence is derived using tools from functional analysis and the boundedness property of Green's kernel. The Galerkin scheme has <span><math><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mi>α</mi></mrow></msup><mo>)</mo></mrow></math></span> order of convergence. Next, the superconvergence of the iterated Galerkin (IG) method is established. The IG method exhibits <span><math><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mi>α</mi><mo>+</mo><msup><mrow><mi>α</mi></mrow><mrow><mo>⁎</mo></mrow></msup></mrow></msup><mo>)</mo></mrow></math></span> order of convergence. Theoretical findings are validated through extensive numerical experiments.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142172411","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 numerical method for Ψ-fractional integro-differential equations by Bell polynomials 用贝尔多项式计算Ψ-分式积分微分方程的数值方法
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-09-11 DOI: 10.1016/j.apnum.2024.09.011
Parisa Rahimkhani
{"title":"A numerical method for Ψ-fractional integro-differential equations by Bell polynomials","authors":"Parisa Rahimkhani","doi":"10.1016/j.apnum.2024.09.011","DOIUrl":"10.1016/j.apnum.2024.09.011","url":null,"abstract":"<div><p>In this work, we focus on a class of Ψ− fractional integro-differential equations (Ψ-FIDEs) involving Ψ-Caputo derivative. The objective of this paper is to derive the numerical solution of Ψ-FIDEs in the truncated Bell series. Firstly, Ψ-FIDEs by using the definition of Ψ− Caputo derivative is converted into a singular integral equation. Then, a computational procedure based on the Bell polynomials, Gauss-Legendre quadrature rule, and collocation method is developed to effectively solve the singular integral equation. The convergence of the approximation obtained in the presented strategy is investigated. Finally, the effectiveness and superiority of our method are revealed by numerical samples. The results of the suggested approach are compared with the results obtained by extended Chebyshev cardinal wavelets method (EChCWM).</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142171641","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
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