Computational and Applied Mathematics最新文献

{"title":"A machine learning framework for efficiently solving Fokker–Planck equations","authors":"Ali Nosrati Firoozsalari, Alireza Afzal Aghaei, Kourosh Parand","doi":"10.1007/s40314-024-02899-w","DOIUrl":"https://doi.org/10.1007/s40314-024-02899-w","url":null,"abstract":"<p>This paper addresses the challenge of solving Fokker–Planck equations, which are prevalent mathematical models across a myriad of scientific fields. Due to factors like fractional-order derivatives and non-linearities, obtaining exact solutions to this problem can be complex. To overcome these challenges, our framework first discretizes the given equation using the Crank-Nicolson finite difference method, transforming it into a system of ordinary differential equations. Here, the approximation of time dynamics is done using forward difference or an L1 discretization technique for integer or fractional-order derivatives, respectively. Subsequently, these ordinary differential equations are solved using a novel strategy based on a kernel-based machine learning algorithm, named collocation least-squares support vector regression. The effectiveness of the proposed approach is demonstrated through multiple numerical experiments, highlighting its accuracy and efficiency. This performance establishes its potential as a valuable tool for tackling Fokker–Planck equations in diverse applications.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"44 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Projection algorithms with adaptive step sizes for multiple output split mixed variational inequality problems","authors":"Tran Van Thang","doi":"10.1007/s40314-024-02896-z","DOIUrl":"https://doi.org/10.1007/s40314-024-02896-z","url":null,"abstract":"<p>We present new iterative algorithms for solving a split convex feasibility problem with multiple output sets involving a monotone mixed variational inequality in real Hilbert spaces. The proposed algorithms follow the Tseng projection method, but with self-adaptive step-sizes that do not depend on the norm of the transfer operator as well as knowledge of a Lipschitz constant. The convergence of the sequences generated by the proposed algorithms is established. We use the proposed algorithms to solve a modified oligopolistic Nash–Cournot equilibrium model. Numerical experiments show that our algorithms are efficient and competitive compared to several recent algorithms.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"7 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Single-machine group scheduling with general linear deterioration and truncated learning effects","authors":"Na Yin, Ming Gao","doi":"10.1007/s40314-024-02881-6","DOIUrl":"https://doi.org/10.1007/s40314-024-02881-6","url":null,"abstract":"<p>In this paper we consider single-machine scheduling problems with group technology, where the group setup times are general linear functions of their starting times and the jobs in the same group have general truncated learning effects. The objective is to minimize the makespan and total completion time, respectively. We show that the makespan minimization remains polynomially solvable. For the total completion time minimization, optimal properties are presented and then we introduce some heuristic algorithms and a branch-and-bound algorithm.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"232 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sufficient conditions for hamiltonian properties of graphs based on the difference of Zagreb indices","authors":"Yuxin Jin, Shuming Zhou, Tao Tian, Kinkar Chandra Das","doi":"10.1007/s40314-024-02909-x","DOIUrl":"https://doi.org/10.1007/s40314-024-02909-x","url":null,"abstract":"<p>A graph invariant, in the sense of graph automorphism, is a mapping from the set of graphs to the reals. Numerous topological indices have been proposed to characterize the topological properties of graphs, and they are widely recognized as graph invariants. Some sufficient conditions in terms of certain topological indices have been suggested to describe hamiltonian properties of graphs, such as Hamiltonicity, traceability, Hamiltonian-connectedness, <i>k</i>-leaf-connectedness, as well as <span>(beta )</span>-deficiency. For a graph <i>G</i>, the first and second Zagreb indices are defined as <span>(M_1(G)= sum nolimits _{uin V(G)} {d_u^2})</span> and <span>(M_2(G)= sum nolimits _{uvin E(G)} {d_u}{d_v})</span>, where <span>(d_u)</span> denotes the degree of vertex <i>u</i> in <i>G</i>. The difference of Zagreb indices of <i>G</i> is defined as <span>(Delta M(G) = {M_2}(G) - {M_1}(G))</span>. In this paper, we suggest some sufficient conditions in terms of <span>(Delta M(G))</span> for graphs to be Hamiltonian, Hamiltonian-connected and <span>(beta )</span>-deficient, respectively.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"53 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Efficient finite element method for 2D singularly perturbed parabolic convection diffusion problems with discontinuous source term","authors":"R. Soundararajan, V. Subburayan","doi":"10.1007/s40314-024-02894-1","DOIUrl":"https://doi.org/10.1007/s40314-024-02894-1","url":null,"abstract":"<p>This article presents a numerical solution for a specific class of 2D parabolic singularly perturbed convection-diffusion problems with a special interior line source. The proposed approach employs the alternating direction implicit type operator splitting streamline-diffusion finite element method (SDFEM), offering a viable solution to alleviate computational complexity and high storage requirements encountered in higher-dimensional problems. The overall stability of the two-step method is established, while a piecewise-uniform Shishkin mesh is employed for spatial domain discretization. By carefully selecting the stabilization parameter, an <span>(varepsilon )</span>-uniform error estimate is derived, accounting for the influence of the time step-interval which is essential to maintain the method’s stability. To validate the theoretical error estimate, numerical investigation are conducted, showcasing the effectiveness of the proposed method. This research contributes to advancing the understanding and numerical treatment of this specific class of 2D parabolic singularly perturbed convection-diffusion problems, shedding light on the intricate dynamics and behavior of the system in the presence of a special interior line source.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"8 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the admissibility of the alpha-order for fuzzy numbers","authors":"Diego García-Zamora, Anderson Cruz, Fernando Neres, Antonio Francisco Roldán López de Hierro, Regivan H. N. Santiago, Humberto Bustince","doi":"10.1007/s40314-024-02885-2","DOIUrl":"https://doi.org/10.1007/s40314-024-02885-2","url":null,"abstract":"<p>The concept of alpha-order has been recently introduced as a binary relation that allows ranking fuzzy sets with bounded support and whose <span>(beta )</span>-cuts are closed subsets with a finite number of connected components. This paper explores some key properties of such alpha-order. Specifically, we will focus on admissibility, a fundamental property for any ranking method defined for fuzzy numbers since it guarantees that such a ranking method is consistent with the usual order on the real line.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"6 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142223531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Neighborhood-related q-rung orthopair fuzzy covering-based rough set models and their applications for multi-attribute decision making","authors":"Linlin Xie, Wei Li, Bin Yang","doi":"10.1007/s40314-024-02889-y","DOIUrl":"https://doi.org/10.1007/s40314-024-02889-y","url":null,"abstract":"<p>In the current intelligent era, with the increasing complexity and diversification of productive practices, it is usually necessary to get a balanced consideration of many aspects of the decision-making problem. One of the most important and popular methods to solve decision problems is multi-attribute decision making (MADM). Traditional MADM problems in <i>q</i>-rung orthopair fuzzy (<i>q</i>-ROF) environment aggregate evaluation information by means of aggregation operators. However, aggregation operators are improper to effectively solve some complicated problems. To settle this problem, we come up with a new method based on neighborhood-related <i>q</i>-ROF covering-based rough set (NR<i>q</i>-ROFCRS) models for MADM problem in this paper. To define these models, several <i>q</i>-ROF logical operators are firstly defined. Next the concepts of <i>q</i>-ROF neighborhood systems of an object, <i>q</i>-ROF minimal and maximal description of an object and <i>q</i>-ROF covering are defined. On this basis, four <i>t</i>-norm-based <i>q</i>-ROF neighborhood operators (T<i>q</i>-ROFNOs) and four overlap function-based <i>q</i>-ROF neighborhood operators (O<i>q</i>-ROFNOs) are proposed. For a finite <i>q</i>-ROF covering, combining four T<i>q</i>-ROFNOs and six <i>q</i>-ROF coverings results in 24 T<i>q</i>-ROFNOs and only sixteen groups of T<i>q</i>-ROFNOs are obtained. We also combine four O<i>q</i>-ROFNOs and six <i>q</i>-ROF coverings and prove that only seventeen groups of O<i>q</i>-ROFNOs are obtained. Then partial order relations among 16 groups of T<i>q</i>-ROFNOs and 17 groups of O<i>q</i>-ROFNOs are discussed, respectively. Moreover, four types of NR<i>q</i>-ROFCRS models are defined based on <i>q</i>-ROF neighborhood operators and the groups and partial order relations of neighborhood-related <i>q</i>-ROF approximate operators are discussed. Finally, a novel method for MADM problems by integrating NR<i>q</i>-ROFCRS models with TOPSIS method is put forward and the effectiveness and the reasonableness of our method are verified by experiments.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"157 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A new approximate descent derivative-free algorithm for large-scale nonlinear symmetric equations","authors":"Xiaoliang Wang","doi":"10.1007/s40314-024-02895-0","DOIUrl":"https://doi.org/10.1007/s40314-024-02895-0","url":null,"abstract":"<p>In this paper, an approximate descent three-term derivative-free algorithm is developed for a large-scale system of nonlinear symmetric equations where the gradients and the difference of the gradients are computed approximately in order to avoid computing and storing the corresponding Jacobian matrices or their approximate matrices. The new method enjoys the sufficient descent property independent of the accuracy of line search strategies and the error bounds of these approximations are established. Under some mild conditions and a nonmonotone line search technique, the global and local convergence properties are established respectively. Numerical results indicate that the proposed algorithm outperforms the other similar ones available in the literature.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"3 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A new robust compact difference scheme on graded meshes for the time-fractional nonlinear Kuramoto–Sivashinsky equation","authors":"Jiawei Wang, Xiaoxuan Jiang, Xuehua Yang, Haixiang Zhang","doi":"10.1007/s40314-024-02883-4","DOIUrl":"https://doi.org/10.1007/s40314-024-02883-4","url":null,"abstract":"<p>In this study, we explore a new robust compact difference method (CDM) on graded meshes for the time-fractional nonlinear Kuramoto–Sivashinsky (KS) equation. This equation exemplifies a fourth-order sub-diffusion equation marked by nonlinearity. Considering the weak singularity often exhibited by exact solutions of time-fractional partial differential equations (TFPDEs) near the initial time, we introduce the L2-1<span>(_{sigma })</span> scheme on graded meshes to discretize the Caputo derivatives. By employing a novel double reduction order approach, we obtain a triple-coupled nonlinear system of equations. To address the nonlinear term <span>(uu_{x})</span>, we use a fourth-order nonlinear CDM, while the second and fourth derivatives in space are treated using the fourth-order linear CDM. We prove the solvability through Browder theorem. Additionally, <span>(alpha )</span>-robust stability and convergence are demonstrated by introducing a modified discrete Grönwall inequality. Finally, we present numerical examples to corroborate the findings of our theoretical analysis.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"108 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"New categories of coverings in terms of rough fuzzy sets","authors":"Mohammed Atef","doi":"10.1007/s40314-024-02882-5","DOIUrl":"https://doi.org/10.1007/s40314-024-02882-5","url":null,"abstract":"<p>In this article, we develop innovative models of multigranulation rough fuzzy sets, utilizing fuzzy <span>(beta )</span>-covering and incorporating a range of techniques such as fuzzy <span>(beta )</span>-neighborhood, fuzzy complementary <span>(beta )</span>-neighborhood, fuzzy <span>(beta )</span>-minimal description, and fuzzy <span>(beta )</span>-maximal description. The axiomatic characteristics of fuzzy <span>(beta )</span>-neighborhoods within the context of fuzzy <span>(beta )</span>-covering based multigranulation rough fuzzy sets (F<span>(beta )</span>CMGRFS) are analyzed. Thus, we introduce seven new classes of F<span>(beta )</span>CMGRFS and investigate their relevant properties. Furthermore, the connections and associations between these techniques are established. Thus, we provide a set of observations and propositions that highlight the value and dissimilarities of our proposed models compared to others. A test example is produced to verify the applicability of the presented strategies and treat MCGDM issues. Finally, we compare the outcomes of our approaches and the existing studies to check the reliability and the validity of our work.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"12 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}