Mathematical Methods in the Applied Sciences最新文献

{"title":"Parallel inertial forward–backward splitting methods for solving variational inequality problems with variational inclusion constraints","authors":"Tran Van Thang,&nbsp;Ha Manh Tien","doi":"10.1002/mma.10356","DOIUrl":"10.1002/mma.10356","url":null,"abstract":"<p>The inertial forward–backward splitting algorithm can be considered as a modified form of the forward–backward algorithm for variational inequality problems with monotone and Lipschitz continuous cost mappings. By using parallel and inertial techniques and the forward–backward splitting algorithm, in this paper, we propose a new parallel inertial forward–backward splitting algorithm for solving variational inequality problems, where the constraints are the intersection of common solution sets of a finite family of variational inclusion problems. Then, strong convergence of proposed iteration sequences is showed under standard assumptions imposed on cost mappings in a real Hilbert space. Finally, some numerical experiments demonstrate the reliability and benefits of the proposed algorithm.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 1","pages":"748-764"},"PeriodicalIF":2.1,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220243","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":"Extinction and stationary distribution of stochastic hepatitis B virus model","authors":"C. Gokila, M. Sambath","doi":"10.1002/mma.10467","DOIUrl":"https://doi.org/10.1002/mma.10467","url":null,"abstract":"In this article, we develop a Hepatitis B virus model with six compartments affected by environmental fluctuations since the Hepatitis B virus produces serious liver infections in the human body, putting many people at high risk. The existence of a global positive solution is shown to prove the positivity of solutions. We demonstrate that the system experiences the extinction property for a specific parametric restriction. Besides that, we obtain the stochastic stability region for the proposed model through the stationary distribution. To determine the appearance and disappearance of infection in the population, we find and analyze the reproduction ratio . In addition, we have verified the condition of the reproduction ratio through the graphical simulations.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"3 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220245","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":"The multigrid discretization of mixed discontinuous Galerkin method for the biharmonic eigenvalue problem","authors":"Jinhua Feng,&nbsp;Shixi Wang,&nbsp;Hai Bi,&nbsp;Yidu Yang","doi":"10.1002/mma.10455","DOIUrl":"10.1002/mma.10455","url":null,"abstract":"<p>The Ciarlet–Raviart mixed method is popular for the biharmonic equations/eigenvalue problem. In this paper, we propose a multigrid discretization based on the shifted-inverse iteration of Ciarlet–Raviart mixed discontinuous Galerkin method for the biharmonic eigenvalue problem. We prove the a priori error estimates of the approximate eigenpairs. We also give the a posteriori error estimates of the approximate eigenvalues and prove the reliability of the estimator and implement adaptive computation. Numerical experiments show that our method can efficiently compute biharmonic eigenvalues.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2635-2654"},"PeriodicalIF":2.1,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220246","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":"Dynamical bifurcations in a delayed fractional-order neural network involving neutral terms","authors":"Chengdai Huang,&nbsp;Lei Fu,&nbsp;Shuang Liu,&nbsp;Jinde Cao,&nbsp;Mahmoud Abdel-Aty,&nbsp;Heng Liu","doi":"10.1002/mma.10434","DOIUrl":"10.1002/mma.10434","url":null,"abstract":"<p>The stability and bifurcations of a fractional-order neural network with a neutral delay are nicely contemplated with the help of the Cramer's rule. The three-neuron neutral-type fractional-order neural network (NTFONN) is firstly constructed. Secondly, the Laplace transform of the Caputo fractional-order derivatives is used. Afterward, using the analytical method of characteristic equations and Cramer's rule, the existence of Hopf bifurcations is obtained. Moreover, it indicates that the neutral delay plays an enormously significant role in remaining network stabilization and controlling the occurrence of Hopf bifurcations in NTFONN. It further detects that the devised NTFONN has outstanding stability performance in comparison with the corresponding integer-order one. Finally, numerical simulations are developed to confirm the feasibility and validity of the obtained results.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2253-2266"},"PeriodicalIF":2.1,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220248","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":"Deep learning solution of optimal reinsurance‐investment strategies with inside information and multiple risks","authors":"Fanyi Peng, Ming Yan, Shuhua Zhang","doi":"10.1002/mma.10465","DOIUrl":"https://doi.org/10.1002/mma.10465","url":null,"abstract":"This paper investigates an optimal investment‐reinsurance problem for an insurer who possesses inside information regarding the future realizations of the claim process and risky asset process. The insurer sells insurance contracts, has access to proportional reinsurance business, and invests in a financial market consisting of three assets: one risk‐free asset, one bond, and one stock. Here, the nominal interest rate is characterized by the Vasicek model, and the stock price is driven by Heston's stochastic volatility model. Applying the enlargement of filtration techniques, we establish the optimal control problem in which an insurer maximizes the expected power utility of the terminal wealth. By using the dynamic programming principle, the problem can be changed to four‐dimensional Hamilton–Jacobi–Bellman equation. In addition, we adopt a deep neural network method by which the partial differential equation is converted to two backward stochastic differential equations and solved by a stochastic gradient descent‐type optimization procedure. Numerical results obtained using TensorFlow in Python and the economic behavior of the approximate optimal strategy and the approximate optimal utility of the insurer are analyzed.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"8 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220249","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":"Mathematical analysis of the two-phase two-component fluid flow in porous media by an artificial persistent variables approach","authors":"Anja Vrbaški,&nbsp;Ana Žgaljić Keko","doi":"10.1002/mma.10454","DOIUrl":"10.1002/mma.10454","url":null,"abstract":"<p>This paper deals with the existence of weak solutions of the system that describes the two-phase two-component fluid flow in porous media. Both two-phase and possible one-phase flow regions are taken into account. Our research is based on a global pressure, an artificial variable that allows us to partially decouple the original equations. As a second primary unknown for the system, we choose the gas pseudo-pressure, a persistent variable which coincides with the gas pressure in the two-phase regions while it does not have physical meaning in one-phase flow regions, when only the liquid phase is present. This allows us to introduce an another persistent variable that is an artificial variable in one-phase flow regions and a physical variable in two-phase flow regions—the capillary pseudopressure. We rewrite the system's equations in a fully equivalent form in terms of the global pressure and the gas-pseudo pressure. In order to prove the existence of weak solutions of obtained system, we also use the capillary pseudo-pressure. By using it, we can decouple obtained equations on the discrete level. This allows us to derive the existence result for weak solutions in more tractable way.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2612-2634"},"PeriodicalIF":2.1,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220252","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":"Barrett's paradox of cooperation in the case of quasi-linear utilities","authors":"Elvio Accinelli,&nbsp;Atefeh Afsar,&nbsp;Filipe Martins,&nbsp;José Martins,&nbsp;Bruno M.P.M. Oliveira,&nbsp;Jorge Oviedo,&nbsp;Alberto A. Pinto,&nbsp;Luis Quintas","doi":"10.1002/mma.10447","DOIUrl":"10.1002/mma.10447","url":null,"abstract":"&lt;p&gt;This paper fits in the theory of international agreements by studying the success of stable coalitions of agents seeking the preservation of a public good. Extending Baliga and Maskin, we consider a model of \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ N $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; homogeneous agents with quasi-linear utilities of the form \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;;&lt;/mo&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {u}_jleft({r}_j;rright)&amp;amp;amp;#x0003D;{r}&amp;amp;amp;#x0005E;{alpha }-{r}_j $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, where \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ r $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is the aggregate contribution and the exponent \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ alpha $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is the elasticity of the gross utility. When the value of the elasticity \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ alpha $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; increases in its natural range \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;0,1&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ left(0,1right) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, we prove the following five main results in the formation of stable coalitions: (i) the gap of cooperation, characterized as the r","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2493-2516"},"PeriodicalIF":2.1,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220247","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":"Inverse problem of reconstructing source term for a class of non‐divergence parabolic equations","authors":"Xu‐Wei Tie, Zui‐Cha Deng","doi":"10.1002/mma.10461","DOIUrl":"https://doi.org/10.1002/mma.10461","url":null,"abstract":"This paper explores an inverse problem pertaining to the determination of a source function in non‐divergence parabolic equations, where the solution is known at a discrete set of points. Being different from other ordinary inverse source problems, which are often dependent on only one variable, the unknown coefficient in this paper not only depends on the space variable but also depends on the time . On the basis of the optimal control framework, the existence of the optimal solution of the control function is proved. The necessary conditions to be satisfied by the optimal solution are given. The convergence of the optimal solution when the mesh parameters tend to zero is obtained. The conjugate gradient method is applied to the inverse problem and some numerical results are presented for various typical test examples.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"3 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220254","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":"Analysis of impulsive Caputo fractional integro-differential equations with delay","authors":"Akbar Zada,&nbsp;Usman Riaz,&nbsp;Junaid Jamshed,&nbsp;Mehboob Alam,&nbsp;Afef Kallekh","doi":"10.1002/mma.10426","DOIUrl":"10.1002/mma.10426","url":null,"abstract":"<p>The main focus of this manuscript is to study an impulsive fractional integro-differential equation with delay and Caputo fractional derivative. The existence solution of such a class of fractional differential equations is discussed for linear and nonlinear case with the help of direct integral method. Moreover, Banach's fixed point theorem and Schaefer's fixed point theorem are use to discuss the uniqueness and at least one solution of the said fractional differential equations, respectively. Some hypothesis and inequalities are utilize to present four different types of Hyers–Ulam stability of the mentioned impulsive integro-differential equation. Example is provide for the illustration of main results.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2102-2121"},"PeriodicalIF":2.1,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220251","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 Laguerre wavelets-based method for solving Fredholm integral equations with weakly singular logarithmic kernel","authors":"Srikanta Behera,&nbsp;Santanu Saha Ray","doi":"10.1002/mma.10405","DOIUrl":"10.1002/mma.10405","url":null,"abstract":"<p>In this study, a wavelet-based collocation scheme has been introduced for solving the linear and nonlinear Fredholm integral equations as well as the system of linear Fredholm integral equations with weakly singular logarithmic kernel. Initially, Laguerre wavelets have been constructed by dilation and translation of Laguerre polynomials. For the numerical solution of the Fredholm integral equations, all the functions have been approximated with respect to the Laguerre wavelets. Then, the proposed linear and nonlinear Fredholm integral equations reduce to systems of linear and nonlinear algebraic equations by utilizing the function approximations. Furthermore, the error estimation and the convergence analysis of the presented method have been discussed. Moreover, the numerical results of the several experiments have also been presented in both graphical and tabular form to describe the accuracy and efficiency of the approached method, and also, to determine the validity of the presented scheme, the approximate solutions and absolute error values are compared with the results obtained by other existing approaches.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"1701-1724"},"PeriodicalIF":2.1,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220253","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}