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Invariant region property of weak Galerkin method for semilinear parabolic equations
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2024-11-28 DOI: 10.1016/j.cam.2024.116412
Mingze Qin, Xiuli Wang, Huifang Zhou
{"title":"Invariant region property of weak Galerkin method for semilinear parabolic equations","authors":"Mingze Qin,&nbsp;Xiuli Wang,&nbsp;Huifang Zhou","doi":"10.1016/j.cam.2024.116412","DOIUrl":"10.1016/j.cam.2024.116412","url":null,"abstract":"<div><div>In this paper, we establish invariant region properties (IRPs) for the time-continuous and full-discrete weak Galerkin (WG) schemes of the semilinear parabolic equations. The scheme employs the semi-implicit scheme in the time direction and <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-<span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> WG method in the space direction, respectively. The full-discrete scheme is proved to preserve the IRP unconditionally on triangular meshes, and the optimal convergence order estimates in both <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norms are obtained for semi-discrete and full-discrete schemes. Some numerical results are presented to validate the theory of IRP and error estimates.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"460 ","pages":"Article 116412"},"PeriodicalIF":2.1,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142759719","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 fixed-time zeroing neural network and its application to path tracking control of wheeled mobile robots
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2024-11-28 DOI: 10.1016/j.cam.2024.116402
Peng Miao , Daoyuan Zhang , Shuai Li
{"title":"A novel fixed-time zeroing neural network and its application to path tracking control of wheeled mobile robots","authors":"Peng Miao ,&nbsp;Daoyuan Zhang ,&nbsp;Shuai Li","doi":"10.1016/j.cam.2024.116402","DOIUrl":"10.1016/j.cam.2024.116402","url":null,"abstract":"<div><div>Based on the current fixed-time stability criteria, a new Lyapunov function is designed to achieve fixed-time stability for the nonlinear dynamical system. It contains an exponential function term which can make the convergence rate faster. This paper gives the proof of our fixed-time stability criterion and estimates the upper bound of convergence time. The upper bound of convergence time is relatively smaller because it is a constant compounded by a two-layer logarithmic function. While, the impact of parameters is analyzed and some strategies for parameter selection are provided. On the basis of this achievement, we give a novel fixed-time zeroing neural network and it is applied into the wheeled mobile robot path tracking problem. Lastly, simulation results show the validity of our methods.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"460 ","pages":"Article 116402"},"PeriodicalIF":2.1,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142748388","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 Levenberg–Marquardt type algorithm with a Broyden-like update technique for solving nonlinear equations
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2024-11-28 DOI: 10.1016/j.cam.2024.116401
Jingyong Tang , Jinchuan Zhou
{"title":"A Levenberg–Marquardt type algorithm with a Broyden-like update technique for solving nonlinear equations","authors":"Jingyong Tang ,&nbsp;Jinchuan Zhou","doi":"10.1016/j.cam.2024.116401","DOIUrl":"10.1016/j.cam.2024.116401","url":null,"abstract":"<div><div>We propose a variant Broyden-like method for solving nonlinear equations. At each iteration, the proposed method solves a Levenberg–Marquardt type equation in which the matrix is updated by the Broyden-like formula. The global convergence ensured by a nonmonotone derivative-free line search is proved without the nonsingularity condition. Moreover, the proposed method has local quadratic convergence under suitable conditions. Numerical experiments show that our method is more effective than the traditional Broyden-like method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"460 ","pages":"Article 116401"},"PeriodicalIF":2.1,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142757127","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 computation of finite-part integrals of highly oscillatory functions 关于计算高度振荡函数的有限部分积分
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2024-11-24 DOI: 10.1016/j.cam.2024.116334
Ruyun Chen, Yu Li, Yongxiong Zhou
{"title":"On computation of finite-part integrals of highly oscillatory functions","authors":"Ruyun Chen,&nbsp;Yu Li,&nbsp;Yongxiong Zhou","doi":"10.1016/j.cam.2024.116334","DOIUrl":"10.1016/j.cam.2024.116334","url":null,"abstract":"<div><div>In this paper, we propose some methods to compute finite-part integral involving hypersingular and highly oscillatory factors. We first write the integral as the Cauchy principle value integral which is computed based on the variable upper limit integral and frequency parameterization. For computing the nonsingular integral, we use the integration by parts and interpolation. On this basis, we get an asymptotic method and a Filon-type method. In order to test the efficiency of the proposed methods and verify the correctness of the proposed theories, some numerical experiments are performed.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"460 ","pages":"Article 116334"},"PeriodicalIF":2.1,"publicationDate":"2024-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142719586","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
Model free data assimilation with Takens embedding
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2024-11-23 DOI: 10.1016/j.cam.2024.116399
Ziyi Wang, Lijian Jiang
{"title":"Model free data assimilation with Takens embedding","authors":"Ziyi Wang,&nbsp;Lijian Jiang","doi":"10.1016/j.cam.2024.116399","DOIUrl":"10.1016/j.cam.2024.116399","url":null,"abstract":"<div><div>In many practical scenarios, the dynamical system is not available and standard data assimilation methods are not applicable. Our objective is to construct a data-driven model for state estimation without the underlying dynamics. Instead of directly modeling the observation operator with noisy observation, we establish the state space model of the denoised observation. Through data assimilation techniques, the denoised observation information could be used to recover the original model state. Takens’ theorem shows that an embedding of the partial and denoised observation is diffeomorphic to the attractor. This gives a theoretical base for estimating the model state using the reconstruction map. To realize the idea, the procedure consists of offline stage and online stage. In the offline stage, we construct the surrogate dynamics using dynamic mode decomposition with noisy snapshots to learn the transition operator for the denoised observation. The filtering distribution of the denoised observation can be estimated using adaptive ensemble Kalman filter, without knowledge of the model error and observation noise covariances. Then the reconstruction map can be established using the posterior mean of the embedding and its corresponding state. In the online stage, the observation is filtered with the surrogate dynamics. Then the online state estimation can be performed utilizing the reconstruction map and the filtered observation. Furthermore, the idea can be generalized to the nonparametric framework with nonparametric time series prediction methods for chaotic problems. The numerical results show the proposed method can estimate the state distribution without the physical dynamical system.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"460 ","pages":"Article 116399"},"PeriodicalIF":2.1,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142748451","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
Fast convergence rates and trajectory convergence of a Tikhonov regularized inertial primal–dual dynamical system with time scaling and vanishing damping 具有时间缩放和阻尼消失的 Tikhonov 正则化惯性基元二元动力系统的快速收敛率和轨迹收敛性
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2024-11-22 DOI: 10.1016/j.cam.2024.116394
Ting Ting Zhu , Rong Hu , Ya Ping Fang
{"title":"Fast convergence rates and trajectory convergence of a Tikhonov regularized inertial primal–dual dynamical system with time scaling and vanishing damping","authors":"Ting Ting Zhu ,&nbsp;Rong Hu ,&nbsp;Ya Ping Fang","doi":"10.1016/j.cam.2024.116394","DOIUrl":"10.1016/j.cam.2024.116394","url":null,"abstract":"<div><div>A Tikhonov regularized inertial primal-dual dynamical system with time scaling and vanishing damping is proposed for solving a linearly constrained convex optimization problem in Hilbert spaces. The system under consideration consists of two coupled second order differential equations and its convergence properties depend upon the decaying speed of the product of the time scaling parameter and the Tikhonov regularization parameter (named the rescaled regularization parameter) to zero. When the rescaled regularization parameter converges slowly to zero, the generated primal trajectory converges strongly to the minimal norm solution of the problem under suitable conditions. When the rescaled regularization parameter converges rapidly to zero, the system enjoys fast convergence rates in the primal–dual gap, the feasibility violation, the objective residual, and the gradient norm of the objective function along the trajectory, and the weak convergence of the trajectory to a primal–dual solution of the linearly constrained convex optimization problem. Finally, numerical experiments are performed to illustrate the theoretical findings.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"460 ","pages":"Article 116394"},"PeriodicalIF":2.1,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705830","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
Convergent and asymptotic expansions of the displacement elastodynamic integral in terms of known functions
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2024-11-22 DOI: 10.1016/j.cam.2024.116395
Chelo Ferreira , José L. López , Ester Pérez Sinusía
{"title":"Convergent and asymptotic expansions of the displacement elastodynamic integral in terms of known functions","authors":"Chelo Ferreira ,&nbsp;José L. López ,&nbsp;Ester Pérez Sinusía","doi":"10.1016/j.cam.2024.116395","DOIUrl":"10.1016/j.cam.2024.116395","url":null,"abstract":"<div><div>The integral <span><math><mrow><msubsup><mrow><mo>∫</mo></mrow><mrow><mn>0</mn></mrow><mrow><mi>∞</mi></mrow></msubsup><mfrac><mrow><msub><mrow><mi>J</mi></mrow><mrow><mi>μ</mi></mrow></msub><mrow><mo>(</mo><mi>r</mi><mi>t</mi><mo>)</mo></mrow><msub><mrow><mi>J</mi></mrow><mrow><mi>ν</mi></mrow></msub><mrow><mo>(</mo><mi>R</mi><mi>t</mi><mo>)</mo></mrow></mrow><mrow><msup><mrow><mi>t</mi></mrow><mrow><mi>α</mi></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>−</mo><mi>s</mi><mo>)</mo></mrow></mrow></mfrac><mi>d</mi><mi>t</mi></mrow></math></span> plays an essential role in the study of several phenomena in the theory of elastodynamics (Ceballos and Prato, 2014). But an exact evaluation of this integral in terms of known functions is not possible. In this paper, we derive an analytic representation of this integral in the form of convergent series of elementary functions and hypergeometric functions. This series have an asymptotic character for either, small values of the variable <span><math><mi>s</mi></math></span>, or for small values of the variables <span><math><mi>r</mi></math></span> and <span><math><mi>R</mi></math></span>. It is derived by using the asymptotic technique designed in Lopez (2008) for Mellin convolution integrals. Some numerical experiments show the accuracy of the approximation supplied by the first few terms of the expansion.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"460 ","pages":"Article 116395"},"PeriodicalIF":2.1,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142748386","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 estimates for a bubble-enriched C0 interior penalty method to a reduced state constrained elliptic optimal control problem 针对减少状态约束的椭圆最优控制问题的气泡富集 C0 内部惩罚法的误差估计
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2024-11-22 DOI: 10.1016/j.cam.2024.116397
Thirupathi Gudi, Pratibha Shakya
{"title":"Error estimates for a bubble-enriched C0 interior penalty method to a reduced state constrained elliptic optimal control problem","authors":"Thirupathi Gudi,&nbsp;Pratibha Shakya","doi":"10.1016/j.cam.2024.116397","DOIUrl":"10.1016/j.cam.2024.116397","url":null,"abstract":"<div><div>In this article, we study a bubble-enriched <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> interior penalty method for the elliptic optimal control problem with pointwise control constraints. We have used the strategy of converting the control constrained optimization problem into a state constrained optimization problem by removing the control variable. The convergence behavior is obtained in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-like energy norm. We present numerical tests to validate our theoretical results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"460 ","pages":"Article 116397"},"PeriodicalIF":2.1,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142719585","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
An efficient fractional-order PDE based image denoising algorithm with optimal adaptive strategy for ultrasound medical image-based diagnostics
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2024-11-22 DOI: 10.1016/j.cam.2024.116400
Yanzhu Zhang , Tingting Liu , Yangquan Chen , Jing Wang , Mingyu Shi
{"title":"An efficient fractional-order PDE based image denoising algorithm with optimal adaptive strategy for ultrasound medical image-based diagnostics","authors":"Yanzhu Zhang ,&nbsp;Tingting Liu ,&nbsp;Yangquan Chen ,&nbsp;Jing Wang ,&nbsp;Mingyu Shi","doi":"10.1016/j.cam.2024.116400","DOIUrl":"10.1016/j.cam.2024.116400","url":null,"abstract":"<div><div>A fractional partial differential denoising model for ultrasound image and its corresponding finite difference optimization solution algorithm are proposed. The model combines the advantages of the total variational and the fourth-order partial differential equation denoising model, which maintains the edge features and avoids the staircase effect in the smoothing region. In addition, the proposed model employs a dynamic fractional edge detection function with a different order for each pixel point, which is able to adapt to the local texture features of different images. Further, the order optimization objective function is given which incorporates the peak signal-to-noise ratio, structural similarity and mean absolute error. The flower pollination algorithm is proposed to find the optimal order. The proposed model is applied to the real ophthalmic ultrasound image to verify the effectiveness.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"460 ","pages":"Article 116400"},"PeriodicalIF":2.1,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142748387","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
Developing and analyzing a FDTD method for simulation of metasurfaces 开发和分析用于模拟超表面的 FDTD 方法
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2024-11-21 DOI: 10.1016/j.cam.2024.116364
Yunqing Huang , Chanjie Li , Jichun Li
{"title":"Developing and analyzing a FDTD method for simulation of metasurfaces","authors":"Yunqing Huang ,&nbsp;Chanjie Li ,&nbsp;Jichun Li","doi":"10.1016/j.cam.2024.116364","DOIUrl":"10.1016/j.cam.2024.116364","url":null,"abstract":"<div><div>Metasurfaces as 2-D metamaterials have a subwavelength thickness. Direct simulation is very challenging since very fine meshes are needed around the metasurfaces. Here we develop the generalized sheet transition conditions (GSTCs) based finite-difference time-domain (FDTD) scheme by treating the metasurface as a zero-thickness plane. The effectiveness of the scheme is illustrated by three representative examples. We raise the open issue on how to establish the numerical stability of such GSTC-based FDTD scheme.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"460 ","pages":"Article 116364"},"PeriodicalIF":2.1,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698399","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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