Pub Date : 2024-07-26DOI: 10.1007/s40314-024-02863-8
Arhrrabi elhoussain, El-Houari Hamza, J. Vanterler da C. Sousa
This research delves into a comprehensive investigation of a class of (Im )-Hilfer generalized fractional nonlinear equation originated from a capillarity phenomenon involving a logarithmic nonlinearity and Dirichlet boundary conditions. The nonlinearity of the problem, in general, do not satisfies the Ambrosetti-Rabinowitz type condition. Using critical point theorem with variational approach and the ((S_{+})) property of the operator, we establish the existence of positive solutions of our problem with respect to every positive parameter (xi ) in appropriate (Im )-fractional spaces. Our main results is novel and its investigation will enhance the scope of the literature on differential equation of (Im )-Hilfer fractional generalized capillary phenomenon with logarithmic nonlinearity.
{"title":"On a class of capillarity phenomenon with logarithmic nonlinearity involving $$theta (cdot )$$ -Laplacian operator","authors":"Arhrrabi elhoussain, El-Houari Hamza, J. Vanterler da C. Sousa","doi":"10.1007/s40314-024-02863-8","DOIUrl":"https://doi.org/10.1007/s40314-024-02863-8","url":null,"abstract":"<p>This research delves into a comprehensive investigation of a class of <span>(Im )</span>-Hilfer generalized fractional nonlinear equation originated from a capillarity phenomenon involving a logarithmic nonlinearity and Dirichlet boundary conditions. The nonlinearity of the problem, in general, do not satisfies the Ambrosetti-Rabinowitz type condition. Using critical point theorem with variational approach and the <span>((S_{+}))</span> property of the operator, we establish the existence of positive solutions of our problem with respect to every positive parameter <span>(xi )</span> in appropriate <span>(Im )</span>-fractional spaces. Our main results is novel and its investigation will enhance the scope of the literature on differential equation of <span>(Im )</span>-Hilfer fractional generalized capillary phenomenon with logarithmic nonlinearity.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141771134","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}
Pub Date : 2024-07-26DOI: 10.1007/s40314-024-02862-9
Xin Wen, Haiming Song, Yutian Li, Zihan Gao
In this study, we explore the valuation challenge posed by American options subject to regime switching, utilizing a model defined by a complex system of parabolic variational inequalities within an infinite domain. The initial pricing model is transformed into a linear complementarity problem (LCP) in a bounded rectangular domain, achieved through the application of a priori estimations and the introduction of an appropriate artificial boundary condition. To discretize the LCP, we employ a finite difference method (FDM), and address the resulting discretized system using a primal-dual active set (PDAS) strategy. The PDAS approach is particularly advantageous for its ability to concurrently determine the option’s price and the optimal exercise boundary. This paper conducts an extensive convergence analysis, evaluating both the truncation error associated with the FDM and the iteration error of the PDAS. Comprehensive numerical simulations are performed to validate the method’s accuracy and efficiency, underscoring its significant potential for application in the field of financial mathematics.
{"title":"A primal-dual active set approach to the valuation of American options in regime-switching models: numerical solutions and convergence analysis","authors":"Xin Wen, Haiming Song, Yutian Li, Zihan Gao","doi":"10.1007/s40314-024-02862-9","DOIUrl":"https://doi.org/10.1007/s40314-024-02862-9","url":null,"abstract":"<p>In this study, we explore the valuation challenge posed by American options subject to regime switching, utilizing a model defined by a complex system of parabolic variational inequalities within an infinite domain. The initial pricing model is transformed into a linear complementarity problem (LCP) in a bounded rectangular domain, achieved through the application of a priori estimations and the introduction of an appropriate artificial boundary condition. To discretize the LCP, we employ a finite difference method (FDM), and address the resulting discretized system using a primal-dual active set (PDAS) strategy. The PDAS approach is particularly advantageous for its ability to concurrently determine the option’s price and the optimal exercise boundary. This paper conducts an extensive convergence analysis, evaluating both the truncation error associated with the FDM and the iteration error of the PDAS. Comprehensive numerical simulations are performed to validate the method’s accuracy and efficiency, underscoring its significant potential for application in the field of financial mathematics.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785128","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}
Pub Date : 2024-07-24DOI: 10.1007/s40314-024-02868-3
Zhenhua Lyu, Lixin Zhou, Junye Ma
In this paper, we obtain a new estimate for the (product) (gamma )-diagonally dominant degree of the Schur complement of matrices. As applications we discuss the localization of eigenvalues of the Schur complement and present several upper and lower bounds for the determinant of strictly (gamma )-diagonally dominant matrices, which generalizes the corresponding results of Liu and Zhang (SIAM J. Matrix Anal. Appl. 27 (2005) 665-674).
在本文中,我们对矩阵舒尔补集的(乘积)((gamma )-对角主导度)进行了新的估计。作为应用,我们讨论了舒尔补集特征值的定位,并给出了严格(gamma )对角主导矩阵行列式的几个上界和下界,这概括了刘和章(SIAM J. Matrix Anal.27 (2005) 665-674).
{"title":"The $$gamma $$ -diagonally dominant degree of Schur complements and its applications","authors":"Zhenhua Lyu, Lixin Zhou, Junye Ma","doi":"10.1007/s40314-024-02868-3","DOIUrl":"https://doi.org/10.1007/s40314-024-02868-3","url":null,"abstract":"<p>In this paper, we obtain a new estimate for the (product) <span>(gamma )</span>-diagonally dominant degree of the Schur complement of matrices. As applications we discuss the localization of eigenvalues of the Schur complement and present several upper and lower bounds for the determinant of strictly <span>(gamma )</span>-diagonally dominant matrices, which generalizes the corresponding results of Liu and Zhang (SIAM J. Matrix Anal. Appl. 27 (2005) 665-674).</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785129","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}
Pub Date : 2024-07-23DOI: 10.1007/s40314-024-02858-5
Rajesh Ranjan Patra, Sarit Maitra
In this article, we discuss sustainable harvesting using a Filippov predator–prey system, which can produce yield and at the same time prevent over-exploitation of bioresources. The model is composed of two subsystems and the dynamics switch from one to the other with the help of a switching condition. We have derived possible equilibria, their existence and stability conditions for the respective subsystems, along with a comprehensive analysis of their phase space. The local and global stability analysis of the two subsystems, with and without harvesting, are studied. Furthermore, for the Filippov system, we have performed bifurcation analysis for several key parameters like predation rate, threshold quantity and prey refuge. Some local and global sliding bifurcations are also observed for the system. The system is shown to have multiple stable steady states or multiple stable sliding cycles for some suitable choice of parameters. Numerical simulations are presented to illustrate the dynamical behaviour of the system.
{"title":"Discontinuous harvesting policy in a Filippov system involving prey refuge","authors":"Rajesh Ranjan Patra, Sarit Maitra","doi":"10.1007/s40314-024-02858-5","DOIUrl":"https://doi.org/10.1007/s40314-024-02858-5","url":null,"abstract":"<p>In this article, we discuss sustainable harvesting using a Filippov predator–prey system, which can produce yield and at the same time prevent over-exploitation of bioresources. The model is composed of two subsystems and the dynamics switch from one to the other with the help of a switching condition. We have derived possible equilibria, their existence and stability conditions for the respective subsystems, along with a comprehensive analysis of their phase space. The local and global stability analysis of the two subsystems, with and without harvesting, are studied. Furthermore, for the Filippov system, we have performed bifurcation analysis for several key parameters like predation rate, threshold quantity and prey refuge. Some local and global sliding bifurcations are also observed for the system. The system is shown to have multiple stable steady states or multiple stable sliding cycles for some suitable choice of parameters. Numerical simulations are presented to illustrate the dynamical behaviour of the system.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141771042","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}
Pub Date : 2024-07-23DOI: 10.1007/s40314-024-02855-8
Abdelkrim Chakib, Ibrahim Khalil
In this paper, we deal with some shape optimization geometrical inverse spectral problems involving the first eigenvalue and eigenfunction of a p-Laplace operator, over a class of open domains with prescribed volume. We first briefly show the existence of the optimal shape design for the (L^p) norm of the eigenfunctions. We carried out the shape derivative calculation of this shape optimization problem using deformation of domains by vector fields. Then we propose a numerical method using lagrangian functional, Hadamard’s shape derivative and gradient method to determine the minimizers for this shape optimization problem. We investigate also numerically the problem of minimizing the first eigenvalue of the p-Laplacian-Dirichlet operator with volume-constraint on domains, using constrained and unconstrained shape optimization formulations. The resulting proposed algorithms of the optimization process are based on the inverse power algorithm (Biezuner et al. 2012) and the finite elements method performed to approximate the first eigenvalue and related eigenfunction. Numerical examples and illustrations are provided for different constrained and unconstrained shape optimization formulations and for various cost functionals to show the efficiency and practical suitability of the proposed approach.
{"title":"On some geometrical eigenvalue inverse problems involving the p-Laplacian operator","authors":"Abdelkrim Chakib, Ibrahim Khalil","doi":"10.1007/s40314-024-02855-8","DOIUrl":"https://doi.org/10.1007/s40314-024-02855-8","url":null,"abstract":"<p>In this paper, we deal with some shape optimization geometrical inverse spectral problems involving the first eigenvalue and eigenfunction of a <i>p</i>-Laplace operator, over a class of open domains with prescribed volume. We first briefly show the existence of the optimal shape design for the <span>(L^p)</span> norm of the eigenfunctions. We carried out the shape derivative calculation of this shape optimization problem using deformation of domains by vector fields. Then we propose a numerical method using lagrangian functional, Hadamard’s shape derivative and gradient method to determine the minimizers for this shape optimization problem. We investigate also numerically the problem of minimizing the first eigenvalue of the p-Laplacian-Dirichlet operator with volume-constraint on domains, using constrained and unconstrained shape optimization formulations. The resulting proposed algorithms of the optimization process are based on the inverse power algorithm (Biezuner et al. 2012) and the finite elements method performed to approximate the first eigenvalue and related eigenfunction. Numerical examples and illustrations are provided for different constrained and unconstrained shape optimization formulations and for various cost functionals to show the efficiency and practical suitability of the proposed approach.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141771043","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}
Pub Date : 2024-07-23DOI: 10.1007/s40314-024-02851-y
Vito Lampret
Several sharp approximations of the generalized-binomial-coefficient function having real arguments are presented on the basis of Stirling’s approximation formula for (Gamma ) function.
{"title":"Accurate approximations of classical and generalized binomial coefficients","authors":"Vito Lampret","doi":"10.1007/s40314-024-02851-y","DOIUrl":"https://doi.org/10.1007/s40314-024-02851-y","url":null,"abstract":"<p>Several sharp approximations of the generalized-binomial-coefficient function having real arguments are presented on the basis of Stirling’s approximation formula for <span>(Gamma )</span> function.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141771039","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}
Pub Date : 2024-07-22DOI: 10.1007/s40314-024-02860-x
Lu-Xin Wang, Yang Cao, Qin-Qin Shen, Chen-Can Zhou
To further accelerate the convergence rate of the recent proposed modified modulus-based matrix splitting (MMMS) iteration method for solving the implicit complementarity problems, by using the two-step iteration methodology, a class of modified two-step modulus-based matrix splitting (MTMMS) iteration methods are studied in this paper. The convergence analyses of the MTMMS iteration method are carefully studied when the system matrix is a positive definite matrix or an (H_+)-matrix. Finally, two numerical experiments are presented. Numerical results show that the proposed MTMMS iteration method performs much better than the existing MMMS iteration method.
{"title":"Modified two-step modulus-based matrix splitting iteration methods for implicit complementarity problems","authors":"Lu-Xin Wang, Yang Cao, Qin-Qin Shen, Chen-Can Zhou","doi":"10.1007/s40314-024-02860-x","DOIUrl":"https://doi.org/10.1007/s40314-024-02860-x","url":null,"abstract":"<p>To further accelerate the convergence rate of the recent proposed modified modulus-based matrix splitting (MMMS) iteration method for solving the implicit complementarity problems, by using the two-step iteration methodology, a class of modified two-step modulus-based matrix splitting (MTMMS) iteration methods are studied in this paper. The convergence analyses of the MTMMS iteration method are carefully studied when the system matrix is a positive definite matrix or an <span>(H_+)</span>-matrix. Finally, two numerical experiments are presented. Numerical results show that the proposed MTMMS iteration method performs much better than the existing MMMS iteration method.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141737816","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}
Pub Date : 2024-07-22DOI: 10.1007/s40314-024-02843-y
Quan Zhou, Yinkun Wang, Lingling Ma, Yicheng Liu
In this work, we propose a piecewise Jacobi–Gauss spectral collocation (JGSC) method for simulating a multi-particle system involving processing delay. Through the use of Jacobi orthogonal approximation and simple Picard iteration, the method obtains the Jacobi series solution of the multi-particle model, allowing us to derive the numerical solution of the processing delay directly. The matrix–vector form of the method helps to obtain the solution parallelly and improves the efficiency significantly. Additionally, the eigenvalues of the iteration’s coefficient matrix are evaluated in order to analyze the convergence of the JGSC method numerically. Numerical experiments illustrate that the JGSC method can keep the high accuracy and efficiency. Furthermore, simulation results of the model indicate that the flocking behavior can only achieved with small enough processing time delays and large enough sizes of the neighborhood.
{"title":"Piecewise Jacobi–Gauss spectral collocation simulations for a multi-particle model involving processing delay","authors":"Quan Zhou, Yinkun Wang, Lingling Ma, Yicheng Liu","doi":"10.1007/s40314-024-02843-y","DOIUrl":"https://doi.org/10.1007/s40314-024-02843-y","url":null,"abstract":"<p>In this work, we propose a piecewise Jacobi–Gauss spectral collocation (JGSC) method for simulating a multi-particle system involving processing delay. Through the use of Jacobi orthogonal approximation and simple Picard iteration, the method obtains the Jacobi series solution of the multi-particle model, allowing us to derive the numerical solution of the processing delay directly. The matrix–vector form of the method helps to obtain the solution parallelly and improves the efficiency significantly. Additionally, the eigenvalues of the iteration’s coefficient matrix are evaluated in order to analyze the convergence of the JGSC method numerically. Numerical experiments illustrate that the JGSC method can keep the high accuracy and efficiency. Furthermore, simulation results of the model indicate that the flocking behavior can only achieved with small enough processing time delays and large enough sizes of the neighborhood.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141771041","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}
Pub Date : 2024-07-19DOI: 10.1007/s40314-024-02854-9
Dragan Stevanović, Mohammad Ghebleh, Gilles Caporossi, Ambat Vijayakumar, Sanja Stevanović
The triangle-degree of a vertex v of a simple graph G is the number of triangles in G that contain v. A simple graph is triangle-distinct if all its vertices have distinct triangle-degrees. Berikkyzy et al. [Discrete Math. 347 (2024) 113695] recently asked whether there exists a regular graph that is triangle-distinct. Here we first showcase the examples of regular, triangle-distinct graphs, and then show that for every natural number k there exists a family of (2^k) regular triangle-distinct graphs, all having the same order and size.
简单图 G 的顶点 v 的三角形度是 G 中包含 v 的三角形的数目。如果一个简单图的所有顶点都有不同的三角形度,那么这个图就是三角形模糊图。Berikkyzy 等人[Discrete Math. 347 (2024) 113695]最近提出了一个问题:是否存在三角形不明显的正则图?在这里,我们首先展示了正则、三角形不明显图的例子,然后证明对于每个自然数 k,都存在一个 (2^k) 正则三角形不明显图的族,它们都具有相同的阶数和大小。
{"title":"On regular triangle-distinct graphs","authors":"Dragan Stevanović, Mohammad Ghebleh, Gilles Caporossi, Ambat Vijayakumar, Sanja Stevanović","doi":"10.1007/s40314-024-02854-9","DOIUrl":"https://doi.org/10.1007/s40314-024-02854-9","url":null,"abstract":"<p>The triangle-degree of a vertex <i>v</i> of a simple graph <i>G</i> is the number of triangles in <i>G</i> that contain <i>v</i>. A simple graph is triangle-distinct if all its vertices have distinct triangle-degrees. Berikkyzy et al. [Discrete Math. 347 (2024) 113695] recently asked whether there exists a regular graph that is triangle-distinct. Here we first showcase the examples of regular, triangle-distinct graphs, and then show that for every natural number <i>k</i> there exists a family of <span>(2^k)</span> regular triangle-distinct graphs, all having the same order and size.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141737815","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}
Pub Date : 2024-07-18DOI: 10.1007/s40314-024-02853-w
Adem Yolcu, Taha Yasin Ozturk, Sadi Bayramov
In this paper, a different approach is used to define a cartesian product on soft sets. This method processes both alternatives and parameters. The notion of the cartesian product is then used to define the idea of a soft relation. The concepts of reflexion, symmetry and transition are defined on the soft relation. Some properties are investigated. Also, the soft function notion is introduced. Various instances are provided as the key characteristics of the structures that are being presented are analyzed. Finally, an application is presented by building a decision making algorithm on the soft relation.
{"title":"A new approach to soft relations and soft functions","authors":"Adem Yolcu, Taha Yasin Ozturk, Sadi Bayramov","doi":"10.1007/s40314-024-02853-w","DOIUrl":"https://doi.org/10.1007/s40314-024-02853-w","url":null,"abstract":"<p>In this paper, a different approach is used to define a cartesian product on soft sets. This method processes both alternatives and parameters. The notion of the cartesian product is then used to define the idea of a soft relation. The concepts of reflexion, symmetry and transition are defined on the soft relation. Some properties are investigated. Also, the soft function notion is introduced. Various instances are provided as the key characteristics of the structures that are being presented are analyzed. Finally, an application is presented by building a decision making algorithm on the soft relation.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141737802","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}