Journal of Computational and Applied Mathematics最新文献

{"title":"High-order numerical schemes based on B-spline for solving a time-fractional Fokker–Planck equation","authors":"Pradip Roul,&nbsp;Trishna Kumari","doi":"10.1016/j.cam.2024.116386","DOIUrl":"10.1016/j.cam.2024.116386","url":null,"abstract":"<div><div>The authors of Jiang (2014), Vong and Wang (2014) and Roul et al. (2022) proposed lower-orders computational techniques for solving a time-fractional Fokker–Planck (TFFP) equation. This paper deals with the design of two high-order computational schemes for the TFFP equation. The first scheme is based on a combination of <span><math><mrow><mi>L</mi><mn>2</mn><mo>−</mo><msub><mrow><mn>1</mn></mrow><mrow><mi>σ</mi></mrow></msub></mrow></math></span> scheme and standard quintic B-spline collocation method, while the second one is based on a combination of <span><math><mrow><mi>L</mi><mn>2</mn><mo>−</mo><msub><mrow><mn>1</mn></mrow><mrow><mi>σ</mi></mrow></msub></mrow></math></span> scheme and a new technique, namely improvised quintic B-spline collocation method. Convergence of the suggested method is analyzed. An illustrative example is provided to demonstrate the applicability and efficiency of the proposed method. The convergence orders of first and second methods are <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>Δ</mi><msup><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>Δ</mi><msup><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>Δ</mi><msup><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>Δ</mi><msup><mrow><mi>x</mi></mrow><mrow><mn>6</mn></mrow></msup><mo>)</mo></mrow><mo>,</mo></mrow></math></span> respectively, where <span><math><mrow><mi>Δ</mi><mi>t</mi></mrow></math></span> and <span><math><mrow><mi>Δ</mi><mi>x</mi></mrow></math></span> are the step-sizes in time and space domain, respectively. We compare the computed results with those obtained by the finite difference method (FDM), compact FDM and quartic B-spline collocation method to justify the advantage of proposed schemes.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"460 ","pages":"Article 116386"},"PeriodicalIF":2.1,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142719102","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":"Double inertial subgradient extragradient algorithm for solving equilibrium problems and common fixed point problems with application to image restoration","authors":"Prasit Cholamjiak ,&nbsp;Zhongbing Xie ,&nbsp;Min Li ,&nbsp;Papinwich Paimsang","doi":"10.1016/j.cam.2024.116396","DOIUrl":"10.1016/j.cam.2024.116396","url":null,"abstract":"<div><div>This paper presents a double inertial method for solving equilibrium problems and common fixed point problems in Hilbert spaces. On the basis of the subgradient extragradient method, we modify the self adaptive rule and use an additional parameter to select appropriate step size. Under reasonable assumptions, we establish both weak and linear convergence properties for the proposed algorithm. Finally, numerical experiments are conducted to validate the rationality and effectiveness of the proposed method over the existing ones in the literature.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"460 ","pages":"Article 116396"},"PeriodicalIF":2.1,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142719101","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 collocation heat polynomials method for one-dimensional inverse Stefan problems","authors":"Orazbek Narbek ,&nbsp;Samat A. Kassabek ,&nbsp;Targyn Nauryz","doi":"10.1016/j.cam.2024.116356","DOIUrl":"10.1016/j.cam.2024.116356","url":null,"abstract":"<div><div>The inverse one-phase Stefan problem in one dimension, aimed at identifying the unknown time-dependent heat flux <span><math><mrow><mi>P</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> with a known moving boundary position <span><math><mrow><mi>s</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, is investigated. A previous study (Kassabek et al., 2021) attempted to reconstruct the unknown heat flux <span><math><mrow><mi>P</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> using the Variational Heat Polynomials Method (VHPM). In this paper, we develop the Collocation Heat Polynomials Method (CHPM) for the reconstruction of the time-dependent heat flux <span><math><mrow><mi>P</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>. This method constructs an approximate solution as a linear combination of heat polynomials, which satisfies the heat equation, with the coefficients determined using the collocation method. To address the resulting ill-posed problem, Tikhonov regularization is applied. As an application, we demonstrate the effectiveness of the method on benchmark problems. Numerical results show that the proposed method accurately reconstructs the time-dependent heat flux <span><math><mrow><mi>P</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, even in the presence of significant noise. The results are also compared with those obtained in Kassabek et al. (2021) using the VHPM.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"460 ","pages":"Article 116356"},"PeriodicalIF":2.1,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142759720","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 time integrators for Generalized Multiscale Finite Element Methods applied to advection–diffusion in high-contrast multiscale media","authors":"Wei Xie ,&nbsp;Juan Galvis ,&nbsp;Yin Yang ,&nbsp;Yunqing Huang","doi":"10.1016/j.cam.2024.116363","DOIUrl":"10.1016/j.cam.2024.116363","url":null,"abstract":"<div><div>Despite recent progress in dealing with advection–diffusion problems in high-contrast multiscale settings, there is still a need for methods that speed up calculations without compromising accuracy. In this paper, we consider the challenges of unsteady diffusion–advection problems in the presence of multiscale high-contrast media. We use the Generalized Multiscale Method (GMsFEM) as the space discretization and pay extra attention to the time solver. Traditional finite-difference methods’ accuracy and stability deteriorate in the presence of high contrast and also with an advection term. Following Contreras et al. (2023), we use exponential integrators to handle the time dependence, fully utilizing the advantages of the generalized multiscale method. For situations dominated by diffusion, our approach aligns with previous work. However, in cases where advection starts to dominate, we introduce a different local generalized eigenvalue problem to build the multiscale basis functions. This adjustment makes things more efficient since the basis functions retain more information related to the advection term. We present experiments to demonstrate the effectiveness of our proposed method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"460 ","pages":"Article 116363"},"PeriodicalIF":2.1,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705831","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 combined integer-valued autoregressive process with actuarial applications","authors":"Xiang Hu ,&nbsp;Jing Yao","doi":"10.1016/j.cam.2024.116384","DOIUrl":"10.1016/j.cam.2024.116384","url":null,"abstract":"<div><div>This paper proposes a modification of a combined integer-valued autoregressive (CINAR) process based on binomial thinning, which is instrumental in modeling higher-order dependence between the number of claims in an insurance portfolio. The modified CINAR process is more general and enjoys stationarity and flexibility in higher-order serial dependence modeling. Two actuarial applications of the proposed process in risk theory and credibility model are explored. As an application to risk theory, we derive the distribution of aggregate claims under a discrete-time collective risk model and examine the effect of high-order dependence on the tail-related risk measures of the aggregate claims. Next, we apply the modified CINAR process to account for the unobserved gamma heterogeneity in determining the dynamics of the predictive credibility premium. A real data analysis shows that our approach provides a superior pattern to the predictive premium calculation when compared to the outcomes of several alternative models.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"459 ","pages":"Article 116384"},"PeriodicalIF":2.1,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142700830","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":"An immersed interface neural network for elliptic interface problems","authors":"Xinru Zhang,&nbsp;Qiaolin He","doi":"10.1016/j.cam.2024.116372","DOIUrl":"10.1016/j.cam.2024.116372","url":null,"abstract":"<div><div>In this paper, a new immersed interface neural network (IINN) is proposed for solving interface problems in a regular domain with jump discontinuities on an embedded irregular interface. This method is introduced in Poisson interface problems, which can also be generalized to solving Stokes interface problems and elliptic interface problems. The main idea is using neural network to approximate the extension of the known jump conditions along the normal lines of the interface and constructing a discontinuity capturing function. With such function, the interface problem with a non-smooth solution can be changed to the problem with a smooth solution. The numerical result is composed of the discontinuity capturing function and the smooth solution. There are four novel features in the present work: (i) the jump discontinuities can be accurately captured; (ii) it is not required to label the mesh around the interface and finding the correction term like Immersed Interface Method (IIM); (iii) it is completely mesh-free for training the discontinuity capturing function; (iv) it preserves second-order accuracy for the solution. The numerical results show that the IINN is comparable and behaves better than the traditional immersed interface method and other neural network methods.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"459 ","pages":"Article 116372"},"PeriodicalIF":2.1,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142699821","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 stochastic Bregman golden ratio algorithm for non-Lipschitz stochastic mixed variational inequalities with application to resource share problems","authors":"Xian-Jun Long,&nbsp;Jing Yang","doi":"10.1016/j.cam.2024.116381","DOIUrl":"10.1016/j.cam.2024.116381","url":null,"abstract":"<div><div>In the study of stochastic mixed variational inequalities(SMVIs), Lipschitz is an indispensable assumption for the convergence analysis. However, practical applications may not satisfy this assumption. In this paper, we propose a stochastic Bregman golden ratio algorithm for solving non-Lipschitz SMVIs. Since our algorithm only requires to calculate one stochastic approximation of the expected mapping per iteration, the computations can be reduced. Under some moderate conditions, we prove the almost surely convergence of the iteration sequence and the <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mn>1</mn><mo>/</mo><mi>K</mi><mo>)</mo></mrow></mrow></math></span> convergence rate, where <span><math><mi>K</mi></math></span> denotes the maximum iteration. Furthermore, we derive the probabilities of large deviation results, which provide a high probability guarantee for the convergence of the proposed algorithm. Numerical experiments on Logistic regression problems and modified entropy regularized LP boosting problems show that our algorithm is competitive compared with some existing algorithms. Finally, we apply our algorithm to solve a non-Lipschitz resource sharing problem.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"459 ","pages":"Article 116381"},"PeriodicalIF":2.1,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142699825","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":"Two sixth-order, L∞ convergent, and stable compact difference schemes for the generalized Rosenau-KdV-RLW equation","authors":"Xin Zhang ,&nbsp;Yiran Zhang ,&nbsp;Qunzhi Jin ,&nbsp;Yuanfeng Jin","doi":"10.1016/j.cam.2024.116382","DOIUrl":"10.1016/j.cam.2024.116382","url":null,"abstract":"<div><div>In this paper, two sixth-order compact finite difference schemes for the generalized Rosenau-KdV-RLW equation are investigated, which utilize novel sixth-order operators. One is a two-level nonlinear difference scheme, while the other is a three-level linearized difference scheme. The schemes both achieve second-order and sixth-order accuracy in time and space, respectively. The proposed two schemes preserve key properties of the original equation in a discrete sense. Numerical results are presented to validate the theoretical findings, demonstrating the efficiency and reliability of the proposed compact approaches. Significantly, the proposed sixth-order operators can be extended to numerical algorithms for other equations.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"459 ","pages":"Article 116382"},"PeriodicalIF":2.1,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142699827","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":"An accelerated decentralized stochastic optimization algorithm with inexact model","authors":"Xuexue Zhang ,&nbsp;Sanyang Liu ,&nbsp;Nannan Zhao","doi":"10.1016/j.cam.2024.116383","DOIUrl":"10.1016/j.cam.2024.116383","url":null,"abstract":"<div><div>This paper considers the decentralized stochastic optimization problems where each node of network has only access to the local large data samples and local functions, which are distributed to the computational nodes. We extend the centralized fast adaptive gradient method with inexact model to deal with the large scale problem in the decentralized manner. Moreover, we propose an accelerated decentralized stochastic optimization algorithm with reconstructing parameter equations and defining new approximate local functions. Further, we provide the convergence analysis of the proposed algorithm and illustrate that our algorithm can achieve both the optimal stochastic oracle complexity and communication complexity that depend on the global condition number. Finally, the numerical experiments validate the convergence results of the proposed algorithm.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"459 ","pages":"Article 116383"},"PeriodicalIF":2.1,"publicationDate":"2024-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142700829","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":"H(curl2)-conforming triangular spectral element method for quad-curl problems","authors":"Lixiu Wang ,&nbsp;Huiyuan Li ,&nbsp;Qian Zhang ,&nbsp;Zhimin Zhang","doi":"10.1016/j.cam.2024.116362","DOIUrl":"10.1016/j.cam.2024.116362","url":null,"abstract":"<div><div>In this paper, we consider the <span><math><mrow><mi>H</mi><mrow><mo>(</mo><msup><mrow><mtext>curl</mtext></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>-conforming triangular spectral element method to solve the quad-curl problems. We first explicitly construct the <span><math><mrow><mi>H</mi><mrow><mo>(</mo><msup><mrow><mtext>curl</mtext></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>-conforming elements on triangles through the contravariant transform and the affine mapping from the reference element to physical elements. These constructed elements possess a hierarchical structure and can be categorized into the kernel space and non-kernel space of the curl operator. We then establish <span><math><mrow><mi>H</mi><mrow><mo>(</mo><msup><mrow><mtext>curl</mtext></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>-conforming triangular spectral element spaces and the corresponding mixed formulated spectral element approximation scheme for the quad-curl problems and related eigenvalue problems. Subsequently, we present the best spectral element approximation theory in <span><math><mrow><mi>H</mi><mrow><mo>(</mo><msup><mrow><mtext>curl</mtext></mrow><mrow><mn>2</mn></mrow></msup><mo>;</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span>-seminorms. Notably, the degrees of polynomials in the kernel space solely impact the convergence rate of the <span><math><msup><mrow><mrow><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm of <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>h</mi></mrow></msub></math></span>, without affecting the semi-norm of <span><math><mrow><mi>H</mi><mrow><mo>(</mo><mtext>curl</mtext><mo>;</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>H</mi><mrow><mo>(</mo><msup><mrow><mtext>curl</mtext></mrow><mrow><mn>2</mn></mrow></msup><mo>;</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span>. This observation enables us to derive eigenvalue approximations from either the upper or lower side by selecting different degrees of polynomials for the kernel space and non-kernel space of the curl operator. Finally, numerical results demonstrate the effectiveness and efficiency of our method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"459 ","pages":"Article 116362"},"PeriodicalIF":2.1,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142699824","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}