Computers & Mathematics with Applications最新文献

{"title":"Numerical study of the non-conservative NET-RAT traffic flow model by path-conservative central-upwind schemes","authors":"Saeed Mohammadian, Zuduo Zheng, Shaoshuai Chu, Alexander Kurganov","doi":"10.1016/j.camwa.2024.12.014","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.014","url":null,"abstract":"Behavioral non-equilibrium hyperbolic traffic models, derived from approximated car-following models with human factors, can lose their conservative form, rendering traditional flux-based numerical methods ineffective. This challenge also applies to the recently proposed behavioral continuum (non-equilibrium traffic model based on risk allostasis theory, that is, NET-RAT) model. This paper is focused on solving the Riemann problem and several other initial-value problems for the novel NET-RAT model in the non-conservative form by path-conservative central-upwind (PCCU) schemes. We design extensive numerical tests considering the unique behavioral properties of the NET-RAT model. The PCCU schemes are then applied to these tests and the obtained results demonstrate that major wave types are effectively and accurately captured. At the same time, the fifth-order scheme, which is constructed using an alternative weighted essentially non-oscillatory (A-WENO) approach, yields substantially sharper resolution than its second-order counterpart. The presented numerical study can facilitate the practical implementation of the NET-RAT model for real-world traffic.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"91 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142911898","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":"Vectorized implementation of primal hybrid FEM in MATLAB","authors":"Harish Nagula Mallesham, Kamana Porwal, Jan Valdman, Sanjib Kumar Acharya","doi":"10.1016/j.camwa.2024.12.017","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.017","url":null,"abstract":"We present efficient MATLAB implementations of the lowest-order primal hybrid finite element method (FEM) for linear second-order elliptic and parabolic problems with mixed boundary conditions in two spatial dimensions. We employ backward Euler and the Crank-Nicolson finite difference scheme for the complete discrete setup of the parabolic problem. All the codes presented are fully vectorized using matrix-wise array operations. Numerical experiments are conducted to show the performance of the software.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"26 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142911856","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":"Semi-analytical algorithm for quasicrystal patterns","authors":"Keyue Sun, Xiangjie Kong, Junxiang Yang","doi":"10.1016/j.camwa.2024.12.016","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.016","url":null,"abstract":"To efficiently simulate the quasicrystal patterns, we present a multi-stage semi-analytically algorithm. Utilizing the operator splitting strategy, we first split the original equation into three subproblems. A second-order five-stage scheme consists of solving four nonlinear ordinary differential equations with half time step and solving a linear partial differential equation with full time step. Using the methods of separation of variables, the nonlinear ODEs have analytical solutions. The linear PDE can also be analytically solved by using the Fourier-spectral method in space. In this sense, our proposed is semi-analytical because we only adopt an approximation in time. In each time step, we only need to compute several analytically solutions in a step-by-step manner. Therefore, the algorithm will be highly efficient and the simulation can be easily implemented. The performance and high efficiency of our proposed algorithm are verified via several simulations. To facilitate the interested readers to develop related researches, a MATLAB code for generating 12-fold quasicrystal patterns is provided in Appendix. We also share the computational code on Code Ocean platform, please refer to <ce:inter-ref xlink:href=\"https://doi.org/10.24433/CO.6028082.v1\" xlink:role=\"http://www.elsevier.com/xml/linking-roles/text/html\" xlink:type=\"simple\">https://doi.org/10.24433/CO.6028082.v1</ce:inter-ref>.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"48 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142911894","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 reproducing kernel particle method (RKPM) algorithm for solving the tropical Pacific Ocean model","authors":"Mostafa Abbaszadeh, Maryam Parvizi, Amirreza Khodadadian, Thomas Wick, Mehdi Dehghan","doi":"10.1016/j.camwa.2024.12.011","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.011","url":null,"abstract":"Meshless methods have become increasingly popular for solving a wide range of problems in both solid and fluid mechanics. In this study, we focus on a meshless numerical approach to solve the tropical Pacific Ocean model, which captures the horizontal velocity and layer thickness of ocean waves, using an advanced meshless Galerkin technique known as the reproducing kernel particle method (RKPM). To address the temporal component in this scheme, we apply a Crank-Nicolson finite difference method, resulting in a semi-discrete formulation. For spatial discretization, we use a kernel-based meshless Galerkin method that integrates the strengths of finite element methods with reproducing kernel particle approximations. We conduct a comprehensive stability analysis and provide an a priori estimate for the semi-discrete solution. Furthermore, we derive error estimates for both the semi-discrete and fully discrete solutions. Finally, we validate the theoretical findings and evaluate the method's efficiency through real-world test cases.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"32 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142911904","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 full linear convergence and optimal complexity of adaptive FEM with inexact solver","authors":"Philipp Bringmann, Michael Feischl, Ani Miraçi, Dirk Praetorius, Julian Streitberger","doi":"10.1016/j.camwa.2024.12.013","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.013","url":null,"abstract":"The ultimate goal of any numerical scheme for partial differential equations (PDEs) is to compute an approximation of user-prescribed accuracy at quasi-minimal computation time. To this end, algorithmically, the standard adaptive finite element method (AFEM) integrates an inexact solver and nested iterations with discerning stopping criteria balancing the different error components. The analysis ensuring optimal convergence order of AFEM with respect to the overall computational cost critically hinges on the concept of R-linear convergence of a suitable quasi-error quantity. This work tackles several shortcomings of previous approaches by introducing a new proof strategy. Previously, the analysis of the algorithm required several parameters to be fine-tuned. This work leaves the classical reasoning and introduces a summability criterion for R-linear convergence to remove restrictions on those parameters. Second, the usual assumption of a (quasi-)Pythagorean identity is replaced by the generalized notion of quasi-orthogonality from Feischl (2022) <ce:cross-ref ref>[22]</ce:cross-ref>. Importantly, this paves the way towards extending the analysis of AFEM with inexact solver to general inf-sup stable problems beyond the energy minimization setting. Numerical experiments investigate the choice of the adaptivity parameters.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"203 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142911902","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":"Unconditional superconvergence analysis of a novel energy dissipation nonconforming Crank-Nicolson FEM for Sobolev equations with high order Burgers' type nonlinearity","authors":"Tiantian Liang, Dongyang Shi","doi":"10.1016/j.camwa.2024.12.010","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.010","url":null,"abstract":"A novel energy dissipation Crank-Nicolson (C-N) fully discrete scheme is established by low order nonconforming <mml:math altimg=\"si1.svg\"><mml:mi>E</mml:mi><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:math> element for solving the Sobolev equations with high order Burgers' type nonlinearity. Firstly, the boundedness of the discrete solution in the broken <mml:math altimg=\"si2.svg\"><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math>-norm is achieved directly by the energy dissipation property without using the known time-space splitting technique in the existing literatures, and its well-posedness is demonstrated by the Brouwer fixed point theorem. Secondly, by utilizing the special characters of nonconforming <mml:math altimg=\"si1.svg\"><mml:mi>E</mml:mi><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:math> element, the unconditional superclose result of order <mml:math altimg=\"si3.svg\"><mml:mi>O</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msup><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo linebreak=\"badbreak\" linebreakstyle=\"after\">+</mml:mo><mml:msup><mml:mrow><mml:mi>τ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy=\"false\">)</mml:mo></mml:math> in the broken <mml:math altimg=\"si2.svg\"><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math>-norm is gained strictly with no restrictions between the spatial partition parameter <ce:italic>h</ce:italic> and the time step <ce:italic>τ</ce:italic>. Moreover, the corresponding global superconvergent error estimate of order <mml:math altimg=\"si3.svg\"><mml:mi>O</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msup><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo linebreak=\"badbreak\" linebreakstyle=\"after\">+</mml:mo><mml:msup><mml:mrow><mml:mi>τ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy=\"false\">)</mml:mo></mml:math> is proved by applying an interpolation post-processing approach. Thirdly, an application to some different finite elements and nonlinear PDEs is discussed, which shows that the proposed scheme and the analysis presented herein can be considered as a general framework to cope with. Lastly, the theoretical results are validated by four numerical examples.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"32 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142884407","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-preserving RERK-FEM for the regularized logarithmic Schrödinger equation","authors":"Changhui Yao, Lei Li, Huijun Fan, Yanmin Zhao","doi":"10.1016/j.camwa.2024.12.009","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.009","url":null,"abstract":"A high-order implicit–explicit (IMEX) finite element method with energy conservation is constructed to solve the regularized logarithmic Schrödinger equation (RLogSE) with a periodic boundary condition. The discrete scheme consists of the relaxation-extrapolated Runge–Kutta (RERK) method in the temporal direction and the finite element method in the spatial direction. Choosing a proper relaxation parameter for the RERK method is the key technique for energy conservation. The optimal error estimates in the <mml:math altimg=\"si1.svg\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>-norm and <mml:math altimg=\"si2.svg\"><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math>-norm are provided without any restrictions between time step size <ce:italic>τ</ce:italic> and mesh size <ce:italic>h</ce:italic> by temporal–spatial splitting technology. Numerical examples are given to demonstrate the theoretical results.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"23 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142884406","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 study of an efficient numerical method for solving the generalized fractional reaction-diffusion model involving a distributed-order operator along with stability analysis","authors":"Muhammad Suliman, Muhammad Ibrahim, Ebrahem A. Algehyne, Vakkar Ali","doi":"10.1016/j.camwa.2024.12.006","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.006","url":null,"abstract":"In this manuscript, we study a generalized fractional reaction-diffusion model involving a distributed-order operator. An efficient hybrid approach is proposed to solve the presented model. The <ce:italic>L</ce:italic>1 approximation is utilized to discretize the time variable, while the mixed finite element method is employed for spatial discretization. A detailed error and stability analysis of the proposed method is provided. Furthermore, we prove that the computational accuracy achieved by the proposed approach is of order <mml:math altimg=\"si1.svg\"><mml:mi mathvariant=\"script\">O</mml:mi><mml:mo maxsize=\"2.4ex\" minsize=\"2.4ex\" stretchy=\"true\">(</mml:mo><mml:msup><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo linebreak=\"badbreak\" linebreakstyle=\"after\">+</mml:mo><mml:msup><mml:mrow><mml:mo maxsize=\"2.4ex\" minsize=\"2.4ex\" stretchy=\"true\">(</mml:mo><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:mi>t</mml:mi><mml:mo maxsize=\"2.4ex\" minsize=\"2.4ex\" stretchy=\"true\">)</mml:mo></mml:mrow><mml:mrow><mml:mn>3</mml:mn><mml:mo linebreak=\"badbreak\" linebreakstyle=\"after\">−</mml:mo><mml:msub><mml:mrow><mml:mi>ξ</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">max</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msup><mml:mo maxsize=\"2.4ex\" minsize=\"2.4ex\" stretchy=\"true\">)</mml:mo></mml:math>. To validate and evaluate the numerical approach, three numerical experiments are conducted, with results presented through graphs and tables.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"11 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142884409","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":"Proving the stability estimates of variational least-squares kernel-based methods","authors":"Meng Chen, Leevan Ling, Dongfang Yun","doi":"10.1016/j.camwa.2024.12.008","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.008","url":null,"abstract":"Motivated by the need for the rigorous analysis of the numerical stability of variational least-squares kernel-based methods for solving second-order elliptic partial differential equations, we provide previously lacking stability inequalities. This fills a significant theoretical gap in the previous work [Comput. Math. Appl. 103 (2021) 1-11], which provided error estimates based on a conjecture on the stability. With the stability estimate now rigorously proven, we complete the theoretical foundations and compare the convergence behavior to the proven rates. Furthermore, we establish another stability inequality involving weighted-discrete norms, and provide a theoretical proof demonstrating that the exact quadrature weights are not necessary for the weighted least-squares kernel-based collocation method to converge. Our novel theoretical insights are validated by numerical examples, which showcase the relative efficiency and accuracy of these methods on data sets with large mesh ratios. The results confirm our theoretical predictions regarding the performance of variational least-squares kernel-based method, least-squares kernel-based collocation method, and our new weighted least-squares kernel-based collocation method. Most importantly, our results demonstrate that all methods converge at the same rate, validating the convergence theory of weighted least-squares in our proven theories.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"258 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142841377","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":"Strong approximation of the time-fractional Cahn–Hilliard equation driven by a fractionally integrated additive noise","authors":"Mariam Al-Maskari, Samir Karaa","doi":"10.1016/j.camwa.2024.12.007","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.007","url":null,"abstract":"In this article, we present a numerical scheme for solving a time-fractional stochastic Cahn–Hilliard equation driven by an additive fractionally integrated Gaussian noise. The model involves a Caputo fractional derivative in time of order <mml:math altimg=\"si1.svg\"><mml:mi>α</mml:mi><mml:mo>∈</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:math> and a fractional time-integral noise of order <mml:math altimg=\"si2.svg\"><mml:mi>γ</mml:mi><mml:mo>∈</mml:mo><mml:mo stretchy=\"false\">[</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">]</mml:mo></mml:math>. Our numerical approach combines a piecewise linear finite element method in space with a convolution quadrature in time, designed to handle both time-fractional operators, along with the <mml:math altimg=\"si3.svg\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>-projection for the noise. We conduct a detailed analysis of both spatially semidiscrete and fully discrete schemes, deriving strong convergence rates through energy-based arguments. The solution's temporal Hölder continuity played a key role in the error analysis. Unlike the stochastic Allen–Cahn equation, the inclusion of the unbounded elliptic operator in front of the cubic nonlinearity in our model added complexity and challenges to the error analysis. To address these challenges, we introduce novel techniques and refined error estimates. We conclude with numerical examples that validate our theoretical findings.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"12 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142841376","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}