{"title":"Numerical analysis of a thermoelastic problem of Moore–Gibson–Thompson type with history dependence in the thermal displacement","authors":"N. Bazarra , J.R. Fernández , R. Quintanilla","doi":"10.1016/j.cam.2024.116317","DOIUrl":"10.1016/j.cam.2024.116317","url":null,"abstract":"<div><div>In this work, we study, from the numerical point of view, a heat conduction model which is described by the history dependent version of the Moore–Gibson–Thompson equation. First, we consider the thermal problem, introducing a fully discrete approximation by means of the finite element method and the implicit Euler scheme. The discrete stability of its solution is proved, and an a priori error analysis is provided, which leads to the linear convergence imposing suitable regularity conditions. Secondly, we deal with the natural extension to the thermoelastic case. Following the analysis of the thermal problem, similar results are shown. Finally, we present some one-dimensional numerical simulations for both problems which demonstrate the accuracy of the approximations and the behavior of the discrete energies and the solutions.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532044","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":"Convergence analysis of a weak Galerkin finite element method on a Shishkin mesh for a singularly perturbed fourth-order problem in 2D","authors":"Shicheng Liu , Xiangyun Meng , Qilong Zhai","doi":"10.1016/j.cam.2024.116324","DOIUrl":"10.1016/j.cam.2024.116324","url":null,"abstract":"<div><div>In this paper, we apply the weak Galerkin (WG) finite element method to solve the singularly perturbed fourth-order boundary value problem in a 2D domain. A Shishkin mesh is used to ensure that the method exhibits uniform convergence, regardless of the singular perturbation parameter. Asymptotically optimal order error estimate in a <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> discrete norm is established for the corresponding WG solutions. Numerical tests are provided to verify the convergence theory.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531790","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":"Non-Intrusive Reduced Basis two-grid method for flow and transport problems in heterogeneous porous media","authors":"Wansheng Gao , Ludovic Chamoin , Insa Neuweiler","doi":"10.1016/j.cam.2024.116321","DOIUrl":"10.1016/j.cam.2024.116321","url":null,"abstract":"<div><div>Due to its non-intrusive nature and ease of implementation, the Non-Intrusive Reduced Basis (NIRB) two-grid method has gained significant popularity in numerical computational fluid dynamics simulations. The efficiency of the NIRB method hinges on separating the procedure into offline and online stages. In the offline stage, a set of high-fidelity computations is performed to construct the reduced basis functions, which is time-consuming but is only executed once. In contrast, the online stage adapts a coarse-grid model to retrieve the expansion coefficients of the reduced basis functions. Thus it is much less costly than directly solving a high-fidelity model. However, coarse grids in heterogeneous porous media of flow models are often accompanied by upscaled hydraulic parameters (e.g. hydraulic conductivity), thus introducing upscaling errors. In this work, we introduce the two-scale idea to the existing NIRB two-grid method: when dealing with coarse-grid models, we also employ upscaled model parameters. Both the discretization and upscaling errors are compensated by the rectification post-processing. The numerical examples involve flow and heat transport problems in heterogeneous hydraulic conductivity fields, which are generated by self-affine random fields. Our research findings indicate that the modified NIRB method can effectively capture the large-scale features of numerical solutions, including pressure, velocity, and temperature. However, accurately retrieving velocity fields with small-scale features remains highly challenging.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Analysis of dependent complementary competing risks data from a generalized inverted family of lifetime distributions under a maximum ranked set sampling procedure with unequal samples","authors":"Liang Wang , Chunfang Zhang , Yogesh Mani Tripathi , Yuhlong Lio","doi":"10.1016/j.cam.2024.116309","DOIUrl":"10.1016/j.cam.2024.116309","url":null,"abstract":"<div><div>This paper explores analysis of a dependent complementary competing risks model when the failure causes are distributed by the proposed generalized inverted family of lifetime distributions. Under maximum ranked set sampling with unequal samples (MRSSU), statistical inference of model parameters and reliability indices is discussed under classical frequentist and Bayesian approaches, respectively. Maximum likelihood estimators along with their existence and uniqueness are obtained for model parameters, and associated approximate confidence intervals are constructed in consequence. Bayesian estimation is also performed with respect to general flexible priors, and the Markov Chain Monte Carlo (MCMC) algorithm is proposed for complex posterior computation. The study further examines classical and Bayesian estimations with order restriction of parameters when additional historical information is available in the MRSSU scenario. Finally, the performance of different results is evaluated through numerical simulations and a real data example is presented for demonstrating the application of our methods.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441065","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 mathematical model for the role of vaccination and treatment in measles transmission in Turkey","authors":"Osman Rasit Isik , Necibe Tuncer , Maia Martcheva","doi":"10.1016/j.cam.2024.116308","DOIUrl":"10.1016/j.cam.2024.116308","url":null,"abstract":"<div><div>A previously developed and analyzed deterministic model for the transmission dynamics of measles, which takes into account the possibility of vaccinated people also contracting the disease, has been developed for Turkey. The model consists of nine compartments. The structural identifiability of the model was examined using software and detailed tables are given assuming that the incidence is given for structural identifiability. As a result of this analysis, the model is found to be structurally identifiable if at least two parameters are given along with the incidence. The parameters in this non-autonomous model are determined by considering the 1970–2021 measles case numbers in Turkey. We realize that the changes in immigration rates in Turkey, especially since the early 2000s, the changes in vaccination rates from 1970 to the present, and the changes in the vaccination rates of susceptible individuals, are significant changes in terms of time, and so we assume that these three parameters are time dependent. The practical identifiability of the model with the determined parameters is examined and it is found that if two parameters are given, all parameters except five parameters are practical identifiable. Unidentified parameters are fixed to a value by taking reference sources into account, and a model with all parameters practically identifiable is achieved. With the obtained values, the associated reproduction number of the model was obtained as 1.07 which means that the disease will persist in Turkey.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532043","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":"Pricing of timer volatility-barrier options under Heston’s stochastic volatility model","authors":"Mijin Ha , Donghyun Kim , Ji-Hun Yoon","doi":"10.1016/j.cam.2024.116310","DOIUrl":"10.1016/j.cam.2024.116310","url":null,"abstract":"<div><div>Timer options are financial instruments that enable investors to exercise their rights on a random maturity date the realized variance reaches the level of variance budget. These options provide a stable investment opportunity for investors under the unpredictable and complex financial markets, such as global financial crisis or COVID-19 pandemic, which can induce the drastic changes of the volatility for the underlying asset. Meanwhile, in the financial markets, investors who invest in standard timer options may face the problems caused by the postponement of the exercising time for too low volatility, compared to standard vanilla options. In this regard, to overcome such disadvantages, we propose timer volatility-barrier options, which are activated and expired when the volatility arrives at a relatively low barrier level, with the original properties of the standard timer options. In this paper, by making use of the method of images, we derive an analytical formulas for the timer volatility-barrier options so that the volatility process can be driven by Heston stochastic volatility model, and verify the pricing accuracy of the timer options by comparing our solutions with those obtained from Monte Carlo simulations. Finally, we conduct numerical studies on the timer volatility-barrier options to examine the pricing sensitivities with respect to the various model parameters, and implement the discussion for pricing formula of double volatility barrier type of the timer options.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441275","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":"Tail moments and tail joint moments for multivariate generalized hyperbolic distribution","authors":"Yang Yang, Guojing Wang, Jing Yao","doi":"10.1016/j.cam.2024.116307","DOIUrl":"10.1016/j.cam.2024.116307","url":null,"abstract":"<div><div>In this paper, we investigate two novel risk measures under the weighted risk aggregation model: Tail Moment (TM) and Tail Joint Moment (TJM). These measures encompass numerous classical risk measures and are capable of quantifying higher-moment risks such as tail skewness and tail kurtosis. Considering the asymmetric and heavy-tailed properties typical of financial and insurance data, we employ the Multivariate Generalized Hyperbolic (MGH) distribution to model risk variables. Within this framework, we derive analytical expressions for the TM and TJM. These results facilitate the precise assessment of portfolio tail risk as well as the tail dependence between risk assets. Furthermore, we present two applications to highlight the benefits and robustness of TM and TJM in risk management and portfolio selection. In the first example, we utilize tail conditional skewness (TCS) and tail conditional kurtosis (TCK) to evaluate the extreme loss risks of assets, which are not typically captured by conventional risk measure such as marginal expected shortfall (MES) and tail variance (TV). In the second example, we concentrate on the dependence of risks in a downside market. Specifically, we use Tail Correlation (TCOR) and Tail Co-skewness (TCOS) to analyze the risk relationships between stocks and the market index during downturns. These risk measures provide crucial insights for portfolio tail risk assessment and hedging against downside market risk.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445771","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}
José A. Ferreira , Mario Grassi , Elías Gudiño , Paula de Oliveira
{"title":"Non-Fickian diffusion enhanced by temperature","authors":"José A. Ferreira , Mario Grassi , Elías Gudiño , Paula de Oliveira","doi":"10.1016/j.cam.2024.116314","DOIUrl":"10.1016/j.cam.2024.116314","url":null,"abstract":"<div><div>In this paper we present a novel mathematical model to describe the permeation of a fluid through a polymeric matrix, loaded with drug molecules, followed by its subsequent desorption. Both phenomena are enhanced by temperature. We deduce energy estimates and stability estimates for the weak solution of the model, showing that this solution of the problem is stable in bounded time intervals. Numerical simulations illustrate how the coupling effects, of viscoelastic properties and thermal external assistance, can have a central role in the design of drug delivery devices.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531789","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 MP-Newton method for computing nonlinear eigenpairs and its application for solving a semilinear Schrödinger equation","authors":"Xudong Yao","doi":"10.1016/j.cam.2024.116315","DOIUrl":"10.1016/j.cam.2024.116315","url":null,"abstract":"<div><div>ln Yao and Zhou (2008), a minimax method for computing nonlinear eigenpairs by calculating critical points of the Lagrange multiplier function is presented. But, the method is slow and can find limited amount of eigenpairs. In this paper, a new general characterization, orthogonal-max characterization, for critical points of the Lagrange multiplier function is suggested. An MP-Newton method for finding orthogonal-max type critical points is designed through analyzing how the minimax method works. The new method becomes fast and able to calculate more nonlinear eigenpairs. Numerical experiment confirms these two progresses. Also, the MP-Newton method inherits the advantages of the minimax method. A convergence result for the method is established. Finally, an application for solving a semilinear Schrödinger equation is discussed.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531792","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":"Analysis of a Crank–Nicolson fast element-free Galerkin method for the nonlinear complex Ginzburg–Landau equation","authors":"Xiaolin Li , Xiyong Cui , Shougui Zhang","doi":"10.1016/j.cam.2024.116323","DOIUrl":"10.1016/j.cam.2024.116323","url":null,"abstract":"<div><div>A fast element-free Galerkin (EFG) method is proposed in this paper for solving the nonlinear complex Ginzburg–Landau equation. A second-order accurate time semi-discrete system is presented by using the Crank–Nicolson scheme for the temporal discretization, and then a meshless fully discrete system is established by using the EFG method for the spatial discretization. In the proposed EFG method, Nitsche’s technique is used to impose the essential boundary conditions in a weak sense, and the reproducing kernel gradient smoothing integration is used to accelerate the calculation. Theoretical errors for the time semi-discrete system and the fully discrete EFG system are analyzed in detail. Optimal error estimates of the fully discrete Crank–Nicolson EFG method are obtained 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. Numerical results validate the theoretical results and the effectiveness of the method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433517","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}