Mathematics and Computers in Simulation最新文献

{"title":"News of IMACS","authors":"","doi":"10.1016/S0378-4754(24)00420-8","DOIUrl":"10.1016/S0378-4754(24)00420-8","url":null,"abstract":"","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531039","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":"Can adaptive prey refuge facilitate species coexistence in Bazykin’s prey–predator model?","authors":"Santana Mondal,&nbsp;Subhas Khajanchi","doi":"10.1016/j.matcom.2024.10.020","DOIUrl":"10.1016/j.matcom.2024.10.020","url":null,"abstract":"<div><div>Bazykin’s prey–predator system with constant and adaptive prey refuge is investigated in this paper. We examine Bazykin’s resource consumer system with exponential growth rate and by employing constant prey refuge we demonstrate that refuge does promote species coexistence. The incorporation of constant prey refuge expands the stability zone for the interior equilibrium. Furthermore, the bifurcation diagram with reference to prey refuge (<span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>r</mi></mrow></msub></math></span>) shows how <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>r</mi></mrow></msub></math></span> influences the system’s behavior from unstable to periodic stability and then to equilibrium stability. Next, we provide a Bazykin’s model with adaptive prey refuge and develop a fitness function for the prey population using refuge as a strategy and in order to obtain the prey’s optimal response to the environment we determine evolutionary stable strategies (ESS). Our model consists of more than one ESS, thus we employ the best response dynamics for the prey strategy. Our analysis showcases that adaptive refuge used by the prey population promotes the coexistence of prey–predator dynamics. Our theoretical analysis is supported by extensive numerical simulations. Bifurcation diagrams with reference to the two most crucial parameters, namely, <span><math><msub><mrow><mi>δ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> (intra-species competition rate among predators) and <span><math><mi>τ</mi></math></span> (the rate at which populations adapt to their environment), are included in the numerical analysis. Species cohabitation along a limit cycle or at an equilibrium is discovered to be dependent on the pace of strategy dynamics and the competition amongst predator species.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530171","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":"Some bivariate options pricing in a regime-switching stochastic volatility jump-diffusion model with stochastic intensity, stochastic interest and dependent jump","authors":"Libin Wang ,&nbsp;Lixia Liu","doi":"10.1016/j.matcom.2024.10.011","DOIUrl":"10.1016/j.matcom.2024.10.011","url":null,"abstract":"<div><div>This paper investigates the performance of bivariate options in the hypothesis of association between two underlying assets. Instead of the classical jump-diffusion process, the volatility of assets and the intensity of Poisson co-jump are both subject to the regime-switching square root process in this price dynamics. The endogenous and exogenous interest rate processes are introduced to examine the effect of interest rate on bivariate options pricing, respectively. An analytic pricing expression of bivariate options are deduced by joint discounted conditional characteristic function. Furthermore, the Fourier cosine expansion method is applied to obtain the approximated solutions of bivariate options price. Simulation and numerical examples are realized to examine the effect of the proposed model, the Fourier cosine expansion method, and the sensitivity of key arguments. The results indicate that embedding stochastic intensity, dependent structure of co-jump, and Markov regime-switching into the pricing dynamics have a significant influence on option pricing, and options prices are robust with respect to the choice of interest rate process.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530247","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":"Determination of emissivity profiles using a Bayesian data-driven approach","authors":"Luca Sgheri ,&nbsp;Cristina Sgattoni ,&nbsp;Chiara Zugarini","doi":"10.1016/j.matcom.2024.10.015","DOIUrl":"10.1016/j.matcom.2024.10.015","url":null,"abstract":"<div><div>In this paper, we explore the determination of a spectral emissivity profile that closely matches real data, intended for use as an initial guess and/or a priori information in a retrieval code. Our approach employs a Bayesian method that integrates the CAMEL (Combined ASTER MODIS Emissivity over Land) emissivity database with the MODIS/Terra＋Aqua Yearly Land Cover Type database. The solution is derived as a convex combination of high-resolution Huang profiles using the Bayesian framework. We test our method on IASI (Infrared Atmospheric Sounding Interferometer) data and find that it outperforms the linear spline interpolation of the CAMEL data and the Huang emissivity database itself.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530192","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 effective numerical approach for solving a system of singularly perturbed differential–difference equations in biology and physiology","authors":"Parvin Kumari ,&nbsp;Satpal Singh ,&nbsp;Devendra Kumar","doi":"10.1016/j.matcom.2024.10.010","DOIUrl":"10.1016/j.matcom.2024.10.010","url":null,"abstract":"<div><div>This study aims to analyze a system of time-dependent singularly perturbed differential–difference equations characterized by small shifts, particularly relevant in neuroscience. We employ Taylor series expansions for approximation to manage the equations’ delay and advance parameters. This method allows for a detailed examination of the complex dynamics, ensuring accuracy and feasibility. To discretize the problem, we use the Crank–Nicolson finite difference method in the time direction on a uniform mesh, combined with a Shishkin-type mesh and cubic <span><math><mi>B</mi></math></span>-spline collocation method in the spatial direction. This integrated approach leverages the strengths of each discretization technique in their respective dimensions, ensuring a robust and highly precise numerical solution. We thoroughly investigate the convergence of our proposed method, demonstrating its nearly second-order accuracy. Numerical experiments on two examples confirm its efficiency and effectiveness in practical applications. Furthermore, this approach is highly adaptable and can be implemented seamlessly in any programming language.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530172","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 and comparison of high-performance computing solvers for minimisation problems in signal processing","authors":"Simone Cammarasana,&nbsp;Giuseppe Patané","doi":"10.1016/j.matcom.2024.10.003","DOIUrl":"10.1016/j.matcom.2024.10.003","url":null,"abstract":"<div><div>Several physics and engineering applications involve the solution of a minimisation problem to compute an approximation of the input signal. Modern hardware and software use high-performance computing to solve problems and considerably reduce execution time. In this paper, different optimisation methods are compared and analysed for the solution of two classes of non-linear minimisation problems for signal approximation and denoising with different constraints and involving computationally expensive operations, i.e., (i) the global optimisers <em>divide rectangle-local</em> and the <em>improved stochastic ranking evolution strategy</em>, and (ii) the local optimisers <em>principal axis</em>, the <em>Limited-memory Broyden, Fletcher, Goldfarb, Shanno</em>, and the <em>constrained optimisation by linear approximations</em>. The proposed approximation and denoising minimisation problems are attractive due to their numerical and analytical properties, and their analysis is general enough to be extended to most signal-processing problems. As the main contribution and novelty, our analysis combines an efficient implementation of signal approximation and denoising on arbitrary domains, a comparison of the main optimisation methods and their high-performance computing implementations, and a scalability analysis of the main algebraic operations involved in the solution of the problem, such as the solution of linear systems and singular value decomposition. Our analysis is also general regarding the signal processing problem, variables, constraints (e.g., bounded, non-linear), domains (e.g., structured and unstructured grids, dimensionality), high-performance computing hardware (e.g., cloud computing, homogeneous vs. heterogeneous). Experimental tests are performed on the CINECA Marconi100 cluster at the 26th position in the “<em>top500</em>” list and consider several parameters, such as functional computation, convergence, execution time, and scalability. Our experimental tests are discussed on real-case applications, such as the reconstruction of the solution of the fluid flow field equation on an unstructured grid and the denoising of a satellite image affected by speckle noise. The experimental results show that <em>principal axis</em> is the best optimiser in terms of minima computation: the efficiency of the approximation is <span><math><mtext>38%</mtext></math></span> with 256 processes, while the denoising has <span><math><mtext>46%</mtext></math></span> with 32 processes.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530170","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 modified two-step optimal iterative method for solving nonlinear models in one and higher dimensions","authors":"Chih-Wen Chang ,&nbsp;Sania Qureshi ,&nbsp;Ioannis K. Argyros ,&nbsp;Francisco I. Chicharro ,&nbsp;Amanullah Soomro","doi":"10.1016/j.matcom.2024.09.021","DOIUrl":"10.1016/j.matcom.2024.09.021","url":null,"abstract":"<div><div>Iterative methods are essential tools in computational science, particularly for addressing nonlinear models. This study introduces a novel two-step optimal iterative root-finding method designed to solve nonlinear equations and systems of nonlinear equations. The proposed method exhibits the optimal convergence, adhering to the Kung-Traub conjecture, and necessitates only three function evaluations per iteration to achieve a fourth-order optimal iterative process. The development of this method involves the amalgamation of two well-established third-order iterative techniques. Comprehensive local and semilocal convergence analyses are conducted, accompanied by a stability investigation of the proposed approach. This method marks a substantial enhancement over existing optimal iterative methods, as evidenced by its performance in various nonlinear models. Extensive testing demonstrates that the proposed method consistently yields accurate and efficient results, surpassing existing algorithms in both speed and accuracy. Numerical simulations, including real-world models such as boundary value problems and integral equations, indicate that the proposed optimal method outperforms several contemporary optimal iterative techniques.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530246","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 convergence analysis for the approximation to the solution of an age-structured population model with infinite lifespan","authors":"Luis M. Abia,&nbsp;Óscar Angulo,&nbsp;Juan Carlos López-Marcos,&nbsp;Miguel Ángel López-Marcos","doi":"10.1016/j.matcom.2024.10.007","DOIUrl":"10.1016/j.matcom.2024.10.007","url":null,"abstract":"<div><div>Considering the numerical approximation of the density distribution for an age-structured population model with unbounded lifespan on a compact interval <span><math><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow></math></span>, we prove second order of convergence for a discretization that adaptively selects its truncated age-interval according to the exponential rate of decay with age of the solution of the model. It appears that the adaptive capacity of the length in the truncated age-interval of the discretization to the infinity lifespan is a very convenient approach for a long-time integration of the model to establish the asymptotic behavior of its dynamics numerically. The analysis of convergence uses an appropriate weighted maximum norm with exponential weights to cope with the unbounded age lifespan. We report experiments to exhibit numerically the theoretical results and the asymptotic behavior of the dynamics for an age-structured squirrel population model introduced by Sulsky.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530193","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 two-parameter Tikhonov regularization for a fractional sideways problem with two interior temperature measurements","authors":"Dang Duc Trong ,&nbsp;Dinh Nguyen Duy Hai ,&nbsp;Nguyen Dang Minh ,&nbsp;Nguyen Nhu Lan","doi":"10.1016/j.matcom.2024.10.013","DOIUrl":"10.1016/j.matcom.2024.10.013","url":null,"abstract":"<div><div>This paper deals with a fractional sideways problem of determining the surface temperature of a heat body from two interior temperature measurements. Mathematically, it is formulated as a problem for the one-dimensional heat equation with Caputo fractional time derivative of order <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow></math></span>, where the data are given at two interior points, namely <span><math><mrow><mi>x</mi><mo>=</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></math></span> and <span><math><mrow><mi>x</mi><mo>=</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>, and the solution is determined for <span><math><mrow><mi>x</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>L</mi><mo>)</mo></mrow><mo>,</mo><mn>0</mn><mo>&lt;</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>&lt;</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>≤</mo><mi>L</mi></mrow></math></span>. The problem is challenging since it is severely ill-posed for <span><math><mrow><mi>x</mi><mo>∉</mo><mrow><mo>[</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>]</mo></mrow></mrow></math></span>. For the ill-posed problem, we apply the Tikhonov regularization method in Hilbert scales to construct stable approximation problems. Using the two-parameter Tikhonov regularization, we obtain the order optimal convergence estimates in Hilbert scales by using both <em>a priori</em> and <em>a posteriori</em> parameter choice strategies. Numerical experiments are presented to show the validity of the proposed method.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530248","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":"Fokker–Planck equation and Feynman–Kac formula for multidimensional stochastic dynamical systems with Lévy noises and time-dependent coefficients","authors":"Qingyan Meng ,&nbsp;Yejuan Wang ,&nbsp;Peter E. Kloeden ,&nbsp;Xiaoying Han","doi":"10.1016/j.matcom.2024.10.014","DOIUrl":"10.1016/j.matcom.2024.10.014","url":null,"abstract":"<div><div>The aim of this paper is to establish a version of the Feynman–Kac formula for the time-dependent multidimensional nonlocal Fokker–Planck equation corresponding to a class of time-dependent stochastic differential equations driven by multiplicative symmetric (or asymmetric) <span><math><mi>α</mi></math></span>-stable Lévy noise. First the forward nonlocal Fokker–Planck equation is derived by the adjoint operator method, overcoming the challenges posed by time-dependent multidimensional nonlinear symmetric <span><math><mi>α</mi></math></span>-stable Lévy noise. Subsequently, the Feynman–Kac formula for the forward multidimensional time-dependent nonlocal Fokker–Planck equation is established by applying techniques for the backward nonlocal Fokker–Planck equations, which is associated with the backward stochastic differential equation driven by the multiplicative symmetric <span><math><mi>α</mi></math></span>-stable Lévy noise. Notably, in the case of asymmetric <span><math><mi>α</mi></math></span>-stable Lévy noise case, the presence of the characteristic function in the nonlocal operator adds complexity to the analysis. Using the Feynman–Kac formula, it is demonstrated that the solution of the forward nonlocal Fokker–Planck equation can be readily simulated through Monte Carlo approximation, especially in scenarios involving long-time simulation settings with large steps. These concepts are illustrated with intriguing examples, and the dynamic evolution of the probability density function corresponding to the stochastic SIS model and the stochastic model for the MeKS network (reflecting the interactions among the MecA complex, ComK and ComS) are investigated over an extended period.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530173","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}