Mathematics and Computers in Simulation最新文献

{"title":"A genetic algorithm approach based on spline quasi-interpolation for solving Fredholm integral equations","authors":"F. El Mokhtari ,&nbsp;M. Lamnii ,&nbsp;D. Barrera","doi":"10.1016/j.matcom.2024.10.033","DOIUrl":"10.1016/j.matcom.2024.10.033","url":null,"abstract":"<div><div>This paper focuses on the approximation of solutions of second kind Fredholm integral equations using non-uniform spline quasi-interpolation. Our aim is to determine the most effective non-uniform partition that provides an optimal numerical solution to the integral equation. To achieve this, we introduce a solution approach based on genetic algorithms, using right approximation of the integral equation’s kernel. We present some numerical examples to show the method’s performance.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579063","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":"Limit cycles in a class of planar discontinuous piecewise quadratic differential systems with a non-regular line of discontinuity (I)","authors":"Dongping He ,&nbsp;Jaume Llibre","doi":"10.1016/j.matcom.2024.10.016","DOIUrl":"10.1016/j.matcom.2024.10.016","url":null,"abstract":"<div><div>In this paper we study the limit cycles which bifurcate from the periodic orbits of the quadratic uniform isochronous center <span><math><mrow><mover><mrow><mi>x</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mo>−</mo><mi>y</mi><mo>+</mo><mi>x</mi><mi>y</mi></mrow></math></span>, <span><math><mrow><mover><mrow><mi>y</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mi>x</mi><mo>+</mo><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span>, when this center is perturbed inside the class of all discontinuous piecewise quadratic polynomial differential systems in the plane with two pieces separated by a non-regular line of discontinuity, which is formed by two rays starting from the origin and forming an angle <span><math><mrow><mi>α</mi><mo>=</mo><mi>π</mi><mo>/</mo><mn>2</mn></mrow></math></span>. Using the Chebyshev theory we prove that the maximum number of hyperbolic limit cycles which can bifurcate from these periodic orbits is exactly 8 using the averaging theory of first order. For this class of discontinuous piecewise differential systems we obtain three more limit cycles than the line of discontinuity is regular, i.e., the case of where the two rays form an angle <span><math><mrow><mi>α</mi><mo>=</mo><mi>π</mi></mrow></math></span>.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579069","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 polynomial basis with a shape parameter for curve and surface modeling","authors":"Bahareh Nouri ,&nbsp;Imre Juhász ,&nbsp;Jamshid Saeidian","doi":"10.1016/j.matcom.2024.10.029","DOIUrl":"10.1016/j.matcom.2024.10.029","url":null,"abstract":"<div><div>Based on Bernstein polynomials, a system of functions with a free parameter is proposed in the space of polynomials of degree at most <span><math><mi>n</mi></math></span>. The system inherits several properties of Bernstein polynomials, such as linear independence, non-negativity, partition of unity and symmetry. This new family of functions are employed to construct control point based parametric curves. The free parameter serves as a shape adjustment parameter, by means of which a one-parameter family of polynomial curves is obtained. The new family of curves is in common with Bézier curves in most of the geometric properties, providing a smooth transition between the Bézier curve and the straight line segment joining the first and last control points. Shape preserving properties, such as monotonicity preservation, as well as length, hodograph and variation diminishing are studied. The proposed basis can also be used to create tensor product surfaces. The extent to which the suggested basis generation method can be applied to other (non-polynomial) function spaces is also being investigated.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579068","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":"Epidemic and unemployment interplay through bi-level multi delayed mathematical model","authors":"Akanksha Rajpal ,&nbsp;Sumit Kaur Bhatia ,&nbsp;Shashank Goel ,&nbsp;Sanyam Tyagi ,&nbsp;Praveen Kumar","doi":"10.1016/j.matcom.2024.10.027","DOIUrl":"10.1016/j.matcom.2024.10.027","url":null,"abstract":"<div><div>An epidemic causes significant financial and economic losses in addition to having negative health effects that result in fatalities.Unemployment is one of the key macroeconomic challenges that governments around the world experience when an epidemic occurs.We have presented a bi-level multi-delay model of epidemics and unemployment to understand and help in alleviating the problem of unemployment while protecting the economy during an epidemic.The epidemic model is the top level of this bi-level mathematical model, and the unemployment model is the lower level.Additionally, the delay in the effect of infection on the unemployed population and the delay in the effect of epidemic-related fatalities on both the employed and unemployed have been taken into consideration.Two equilibrium points, infection-free and interior equilibrium points, have been found.We have obtained the basic reproduction number using the Next Generation Matrix (NGM) methodology.We have also established linear stability analysis around the infection-free and interior equilibrium points, as well as properties of Hopf bifurcation and Lyapunov stability analysis around the interior equilibrium point.Finally, we have conducted numerical simulations to validate the results of our analysis.A time frame for the delays to maintain the system’s stability has been obtained, or else it will adopt instability and it will become very challenging to control unemployment.We propose that the governments implement lockdowns to restrict public social interactions in order to lower the infection rate.We have demonstrated that in order for lockdown measures to effectively reduce infections without driving up unemployment, lowering the incidence of infection-related mortality is essential.It is suggested that adequate and timely treatment be provided in order to control infection-induced mortality.In order to prevent unemployment and infection, it is also suggested that companies offer their employees the chance to work from home. To demonstrate the applicability of our work, we have employed model calibration to fit our model to the real data of COVID-19 impacted people in India, as well as an investigation of calibrated model’s dynamics due to delays has been done.This research will help tackle the serious problem of unemployment during an epidemic, which will spur general economic expansion.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579070","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":"Nonlinear dynamics of a Darwinian Ricker system with strong Allee effect and immigration","authors":"Karima Mokni ,&nbsp;Halima Ben Ali ,&nbsp;Bapan Ghosh ,&nbsp;Mohamed Ch-Chaoui","doi":"10.1016/j.matcom.2024.10.017","DOIUrl":"10.1016/j.matcom.2024.10.017","url":null,"abstract":"<div><div>In this paper, we investigate the complex dynamics of a Darwinian Ricker system through a comprehensive qualitative and dynamical analysis. Our research shows that the system exhibits Neimark–Sacker bifurcation, period-doubling bifurcation, and codimension-two bifurcations associated with 1:2, 1:3, and 1:4 resonances. These findings are derived using bifurcation and center manifold theories. We numerically illustrate all bifurcation results and chaotic features, providing a thorough understanding of the system’s behavior. This detailed examination of the Darwinian Ricker system, with a focus on the interplay between immigration and the strong Allee effect, enhances our understanding of the intricate mechanisms driving population dynamics. Furthermore, it highlights the significant implications for ecological modeling, particularly in predicting ecosystem responses to external perturbations such as climate change and species invasions.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579071","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":"Computational insights into tumor invasion dynamics: A finite element approach","authors":"Saba Irum ,&nbsp;Naif Almakayeel ,&nbsp;Wejdan Deebani","doi":"10.1016/j.matcom.2024.10.026","DOIUrl":"10.1016/j.matcom.2024.10.026","url":null,"abstract":"<div><div>The finite element scheme is proposed and analyzed for the solution of an acid-mediated tumor invasion model. The reaction–diffusion equation shows the evolution in the tumor cell density, <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span> ions concentration, and healthy tissue density over time. The coupled non-linear partial differential equations are discretized in time with the implicit Euler method and in space with standard Galerkin finite element. To solve the non-linear and coupled terms of the system a fixed point iteration scheme is presented. Moreover, a mass-lumped scheme is adopted to reduce the computation cost. The cut-off method is used to compute the bounded solutions of the PDEs. Finally, The effects of proliferation rate and healthy tissue degradation rate are investigated.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586322","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":"The study of non-constant steady states and pattern formation for an interacting population model in a spatial environment","authors":"R.P. Gupta,&nbsp;Shristi Tiwari,&nbsp;Arun Kumar","doi":"10.1016/j.matcom.2024.10.022","DOIUrl":"10.1016/j.matcom.2024.10.022","url":null,"abstract":"<div><div>This manuscript accounts for an investigation of the complex dynamics of a spatial model for interacting populations. We discuss the existence and boundedness of solutions for the proposed spatio-temporal system. The global stability of the co-existing steady state of the proposed system is analyzed with the help of a suitable Lyapunov function. We provide results on the existence and non-existence of positive non-constant solutions of the model. The priori estimate for the positive steady state is obtained for the nonexistence of the non-constant positive steady state by using the maximum principle. The existence of a non-constant positive steady state is studied with the help of Leray–Schauder degree theory. The stability and Hopf bifurcation are briefly revisited for the co-existing steady state in the corresponding temporal model, where a bubble-like structure is observed. The onset of Hopf bifurcation has been analyzed, and different conditions for the formation of the Turing pattern have been established through diffusion-driven instability analysis. Numerical simulations are performed in detail to figure out the effects of saturated harvesting on Turing patterns. The Turing as well as non-Turing patterns in their respective domains are also examined. Finally, the criteria of Turing–Hopf bifurcation is briefly demonstrated with relevant numerical examples and corresponding plots that give a better illustration of this work.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554917","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":"Complex dynamics of an SIHR epidemic model with variable hospitalization rate depending on unoccupied hospital beds","authors":"Chunping Jia ,&nbsp;Xia Wang ,&nbsp;Yuming Chen","doi":"10.1016/j.matcom.2024.10.023","DOIUrl":"10.1016/j.matcom.2024.10.023","url":null,"abstract":"<div><div>In this paper, we propose an <strong>susceptible–infectious–hospitalized–recovered</strong> (SIHR) epidemic model with a nonlinear hospitalization rate depending on the number of unoccupied hospital beds. Note that the number of all hospital beds is used as a measure of all available medical resources. The basic reproduction number is calculated using the next-generation matrix method. We analyze the existence of endemic equilibria and discuss the global stability of the disease-free equilibrium. Existence and stability of endemic equilibria indicate possible occurrences of bifurcations. We confirm the appearance of backward bifurcation, saddle–node bifurcation, Hopf bifurcation, and Bogdanov–Takens bifurcation using normal form theory and central manifold theory. Numerical simulations show that the dynamic behavior of the model undergoes a transition from forward bifurcation to backward bifurcation and saddle–node bifurcation when the number of total hospital beds is reduced. Our findings suggest that when the number of total hospital beds falls below a threshold, backward bifurcation will occur, meaning that the disease cannot be eliminated even if the basic reproduction number is below unity. Therefore, the number of hospital beds should be increased beyond the bed threshold during an outbreak of a disease, which has important implications for disease control.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142571529","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 adaptive positive preserving numerical scheme based on splitting method for the solution of the CIR model","authors":"Minoo Kamrani ,&nbsp;Erika Hausenblas","doi":"10.1016/j.matcom.2024.10.021","DOIUrl":"10.1016/j.matcom.2024.10.021","url":null,"abstract":"<div><div>This paper aims to investigate an adaptive numerical method based on a splitting scheme for the Cox–Ingersoll–Ross (CIR) model. The main challenge associated with numerically simulating the CIR process lies in the fact that most existing numerical methods fail to uphold the positive nature of the solution. Within this article, we present an innovative adaptive splitting scheme. Due to the existence of a square root in the CIR model, the step size is adaptively selected to ensure that, at each step, the value under the square-root does not fall under a given positive level and it is bounded. Moreover, an alternate numerical method is employed if the chosen step size becomes excessively small or the solution derived from the splitting scheme turns negative. This alternative approach, characterized by convergence and positivity preservation, is called the “backstop method”.</div><div>Furthermore, we prove the proposed adaptive splitting method ensures the positivity of solutions in the sense that it would be possible to find an interval such that for all stepsizes belong, the probability of using the backstop method can be small. Therefore, the proposed adaptive splitting scheme avoids using the backstop method with arbitrarily high probability. We prove the convergence of the scheme and analyze the convergence rate. Finally, we demonstrate the applicability of the scheme through some numerical simulations, thereby corroborating our theoretical findings.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142571530","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":"IMACS Calendar of Events","authors":"","doi":"10.1016/S0378-4754(24)00421-X","DOIUrl":"10.1016/S0378-4754(24)00421-X","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":"142531040","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}