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Applied Numerical Mathematics最新文献

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A uniformly convergent analysis for multiple scale parabolic singularly perturbed convection-diffusion coupled systems: Optimal accuracy with less computational time 多尺度抛物线奇异扰动对流扩散耦合系统的均匀收敛分析：用更少的计算时间获得最佳精度
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-09-25 DOI: 10.1016/j.apnum.2024.09.020
{"title":"A uniformly convergent analysis for multiple scale parabolic singularly perturbed convection-diffusion coupled systems: Optimal accuracy with less computational time","authors":"","doi":"10.1016/j.apnum.2024.09.020","DOIUrl":"10.1016/j.apnum.2024.09.020","url":null,"abstract":"<div><div>This study addresses time-dependent multiple-scale reaction-convection-diffusion initial boundary value systems characterized by strong coupling in the reaction matrix and weak coupling in the convection terms for a locally optimal accurate solution. The discrete problem, which typically loses its tridiagonal structure, expands its bandwidth to four in such coupled systems, resulting in a substantial computational load. Our objective is to mitigate this computational burden through a splitting approach that transforms the non-tridiagonal matrix into a tridiagonal form while maintaining the consistency, local optimal accuracy in space, and stability of the numerical scheme. We employ equidistributed non-uniform grids, guided by a carefully chosen monitor function, to approximate the continuous space domain. The discretization strategy targets local optimal linear accuracy across space and time on the domain's interior points. In addition, we have also provided the global convergence analysis of the present splitting approach, mathematically. The mathematical evidence is also obtained from the numerical experiments by comparing the splitting approach (either diagonal or triangular forms) of the reaction matrix to its coupled form. The results strongly confirm the effectiveness of this approach in delivering uniform linear accuracy, based on the present problem discretizations while significantly reducing the computational costs.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322448","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
Stability analysis and error estimates of implicit-explicit Runge-Kutta least squares RBF-FD method for time-dependent parabolic equation 时变抛物方程的隐式-显式 Runge-Kutta 最小二乘 RBF-FD 方法的稳定性分析和误差估计
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-09-23 DOI: 10.1016/j.apnum.2024.09.018
{"title":"Stability analysis and error estimates of implicit-explicit Runge-Kutta least squares RBF-FD method for time-dependent parabolic equation","authors":"","doi":"10.1016/j.apnum.2024.09.018","DOIUrl":"10.1016/j.apnum.2024.09.018","url":null,"abstract":"<div><div>In this paper, for the time-dependent parabolic equations defined on complex geometries domain, we develop and analyze the least-squares radial basis function finite difference method (RBF-FD) coupled with the implicit-explicit Runge-Kutta (IMEX-RK) time discretization up to third order accuracy, which improves stability and accuracy. We derive the absolute stability region and the optimal time-step constraint for four kinds of IMEX-RK schemes. Compared to the traditional explicit or implicit time discretization, these are not trivial. Under a wide time-step constraint, the stability and the error estimates in <span><math><msub><mrow><mi>l</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-norm are established. Finally, several numerical experiments on the regular domain and non-convex domain are performed to validate the theoretical analysis.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322450","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 weak Galerkin finite element method for fourth-order parabolic singularly perturbed problems on layer adapted Shishkin mesh 层适配 Shishkin 网格上四阶抛物线奇异扰动问题的弱 Galerkin 有限元方法
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-09-23 DOI: 10.1016/j.apnum.2024.09.019
{"title":"A weak Galerkin finite element method for fourth-order parabolic singularly perturbed problems on layer adapted Shishkin mesh","authors":"","doi":"10.1016/j.apnum.2024.09.019","DOIUrl":"10.1016/j.apnum.2024.09.019","url":null,"abstract":"<div><div>In this paper, we propose a weak Galerkin finite element approximation for a class of fourth-order singularly perturbed parabolic problems. The problem exhibits boundary layers and so we have considered layer adapted triangulations, in particular Shishkin triangular mesh in the spatial domain. For temporal discretization, we utilize the Crank-Nicolson scheme on a uniform mesh. Stability and error estimates along with the uniform convergence of the method has been proved. Numerical examples are included which verifies our analysis.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322451","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
Weak Galerkin finite element method with the total pressure variable for Biot's consolidation model 采用总压力变量的弱伽勒金有限元法用于毕奥特固结模型
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-09-19 DOI: 10.1016/j.apnum.2024.09.017
{"title":"Weak Galerkin finite element method with the total pressure variable for Biot's consolidation model","authors":"","doi":"10.1016/j.apnum.2024.09.017","DOIUrl":"10.1016/j.apnum.2024.09.017","url":null,"abstract":"<div><div>In this work, we develop a weak Galerkin method for the three-field Biot's consolidation model. The key idea is to consider the total pressure variable. We employ the stable pair of weak Galerkin finite elements to discretize the displacement and total pressure, and use totally discontinuous weak functions to approximate pressure in a semi-discrete scheme. Then, we give the fully discrete scheme based on the backward Euler method in time. Furthermore, we prove the well-posedness of the numerical schemes and derive the optimal error estimates for three variables in their nature norms. Our theoretical results are independent of the Lamé constant <em>λ</em> and the storage coefficient <span><math><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>. Finally, some experiments that employ different polynomial degrees and polygonal meshes are presented to demonstrate the efficiency and stability of the weak Galerkin method.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142313014","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
Supercloseness of the NIPG method on a Bakhvalov-type mesh for a singularly perturbed problem with two small parameters 两个小参数奇异扰动问题的巴赫瓦洛夫型网格上 NIPG 方法的超封闭性
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-09-19 DOI: 10.1016/j.apnum.2024.09.016
{"title":"Supercloseness of the NIPG method on a Bakhvalov-type mesh for a singularly perturbed problem with two small parameters","authors":"","doi":"10.1016/j.apnum.2024.09.016","DOIUrl":"10.1016/j.apnum.2024.09.016","url":null,"abstract":"<div><div>In this paper, the nonsymmetric interior penalty Galerkin (NIPG) method on a Bakhvalov-type mesh is proposed for a singularly perturbed problem with two small parameters. In order to reflect the behavior of layers more accurately, a balanced norm, rather than the common energy norm, is introduced. By selecting special penalty parameters at different mesh points, we establish the supercloseness of <span><math><mi>k</mi><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> order, and prove an optimal order of uniform convergence in a balanced norm. Numerical experiments are proposed to confirm our theoretical results.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142313013","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
Error analysis of positivity-preserving energy stable schemes for the modified phase field crystal model 修正相场晶体模型的保正能量稳定方案的误差分析
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2024-09-18 DOI: 10.1016/j.apnum.2024.09.010
{"title":"Error analysis of positivity-preserving energy stable schemes for the modified phase field crystal model","authors":"","doi":"10.1016/j.apnum.2024.09.010","DOIUrl":"10.1016/j.apnum.2024.09.010","url":null,"abstract":"<div><div>In this paper, we introduce second-order numerical schemes for the modified phase field crystal (MPFC) model that are decoupled, linear, positivity-preserving, and unconditionally energy-stable. These schemes adopt a positivity-preserving auxiliary variable method to explicitly handle the nonlinear potential function, resulting in decoupled linear systems with constant coefficients at each time step. We rigorously demonstrate that the auxiliary variables remain positive throughout all time steps and prove the unconditionally energy stability of these schemes. The stability pertains to a discrete modified energy, rather than the original free energy or the pseudo energy of the MPFC system. Moreover, a detailed error analysis is provided. A series of numerical experiments are conducted to validate the accuracy and efficiency of our proposed schemes.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142313015","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 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
{"title":"A novel least squares approach generating approximations orthogonal to the null space of the operator","authors":"","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
{"title":"A comparative study on numerical methods for Fredholm integro-differential equations of convection-diffusion problem with integral boundary conditions","authors":"","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
{"title":"Exact solution for a discrete-time SIR model","authors":"","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
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
{"title":"Numerical solution for a generalized form of nonlinear cordial Volterra integral equations using quasilinearization and Legendre-collocation methods","authors":"","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
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