Mathematics and Computers in Simulation最新文献

This paper considers an efficient and accurate spectral deferred correction (SDC) method for the initial value problem (IVP) with Caputo–Hadamard derivative. We first apply the basic idea of the SDC method to derive the numerical scheme. Then the iteration matrix which is the key to convergence of the proposed scheme can be obtained for the linear problem. Detailed computation of history term is presented using the spectral collocation method based on mapped Jacobi log orthogonal functions (MJLOFs). Finally, numerical simulations for both linear and nonlinear cases are shown to verify the feasibility and efficiency of the proposed method.

This paper studies the global dynamics of an SEIR (Susceptible–Exposed–Infectious–Recovered) model with nonlocal diffusion. We show the model’s well-posedness, proving the solutions’ existence, uniqueness, and positivity, along with a disease-free equilibrium. Next, we prove that the model admits the global threshold dynamics in terms of the basic reproduction number $R_0$, defined as the spectral radius of the next-generation operator. We show that the solution map has a global compact attractor, offering insights into long-term dynamics. In particular, the analysis shows that for $R_0<1$, the disease-free equilibrium is globally stable. Using the persistence theory, we show that there is an endemic equilibrium point for $R_0>1$. Moreover, by constructing an appropriate Lyapunov function, we establish the global stability of the unique endemic equilibrium in two distinct scenarios.

The frequency and severity of extreme events have increased in recent years in many areas. In the context of risk management for insurance companies, reinsurance provides a safe solution as it offers coverage for large claims. This paper investigates the impact of dependent extreme losses on ruin probabilities under four types of reinsurance: excess of loss, quota share, largest claims, and ecomor. To achieve this, we use the dynamic GARCH-EVT-Copula combined model to fit the specific features of claim data and provide more accurate estimates compared to classical models. We derive the surplus processes and asymptotic ruin probabilities under the Cramér–Lundberg risk process. Using a numerical example with real-life data, we illustrate the effects of dependence and the behavior of reinsurance strategies for both insurers and reinsurers. This comparison includes risk premiums, surplus processes, risk measures, and ruin probabilities. The findings show that the GARCH-EVT-Copula model mitigates the over- and under-estimation of risk associated with extremes and lowers the ruin probability for heavy-tailed distributions.

This study presents a meticulous investigation into the intricate dynamics of a Fe${}_3$O${}_4$(25%)–Al${}_2$O${}_3$(50%)–ZnO(25%)/water ternary hybrid nanofluid within the framework of the Darcy–Forchheimer model, inclusive of heat source and suction/injection phenomena on two stretching surfaces. The governing partial differential equations are transformed into ordinary differential equations by strategically applying similarity variables. These equations are then solved using the efficient analytical approach of the Homotopy Analysis Method (HAM) and numerically using the implicit finite difference-based Keller Box Method (KBM). We further compare the solutions obtained through HAM with the numerical results from the KBM approach. The inquiry discerns those pivotal parameters such as porosity ($Pm$) and magnetic ($M$) amplifying the velocity profile ($g$), while parameters including Reynolds number ($Re$), inertia coefficient ($Fr$), rotational ($Ro$), and stretching ($\alpha$) manifest diminishing effects. Furthermore, the study reveals a direct correlation between temperature escalation and the amplification of Eckert number ($Ec$), magnetic ($M$), radiation ($R$), heat source ($Q$), and stretching ($\alpha$) parameters. In the case of suction applied to the lower and upper surfaces, the velocity profiles $f^{\prime }$ and $g$, decrease whereas for injection, the opposite trend is observed. When there is suction at the upper surface the temperature profile decreases, but for suction at the upper surface the same increases. However, when there is injection, a reverse pattern is observed. Compared to water, suspension of nanoparticles with a 5% volume fraction of spheres, cylinders, platelets, and blades achieves 13%, 23%, 27%, and 36% heat transfer rates, respectively. This research provides crucial insights into nanofluid flow and heat transfer, with significant implications for various technological applications.

The shorter lifecycle and faster upgrading of the product make the potential demand change rapidly, thereby pricing based on market changes is critical to increasing profits. In response to changes in the potential demand, we present a dynamic surge pricing model that characterizes sales trajectories and gradient pricing. We introduce the Lotka–Volterra system to construct the sale-forecast system and prove its effectiveness in predicting the product lifecycle curve that reflects the change of the potential demand. In contrast to the linear demand function, we propose a gradient pricing mechanism based on marginal sales and total sales to describe the relationship between price and potential demand throughout the life cycle. Particularly, the dynamic surge pricing model degrades to Cournot model in the maturity phase of the market. We characterize the dynamic equilibrium and conduct the sensitivity analysis of parameters, showing that the dynamic surge pricing model outperforms Cournot model in terms of profit. A numerical example illustrates that the profit of the dynamic surge pricing model is nearly 21.82% higher than that of Cournot model.

The mixed fractional Brownian motion ($mfBm$) has gained popularity in finance because it can effectively model long-range dependence, self-similarity, and is arbitrage-free. This paper focuses on $mfBm$ with jumps modeled by the Poisson process and derives an analytical formula for valuing geometric Asian options. Additionally, approximate closed-form solutions for pricing arithmetic Asian options and arithmetic Asian power options are obtained. Numerical examples are provided to demonstrate the accuracy of these formulas, which rely on a convenient approximation of the option strike price. The proposed approximation demonstrates significantly higher computational efficiency compared to Monte Carlo simulation.

A new Discrete Ordinate-Lattice Boltzmann Method (DO-LBM) is developed by combining DOM and LBM to analyze radiative heat transfer in a two-dimensional irregular enclosure including absorbing, emitting, and scattering media. The accuracy of the proposed method was verified through Chapman-Enskog multi-scale expansion, and non-negativity analysis of the equilibrium distribution function was performed by introducing similarity numbers. Two-dimensional irregular enclosure including curved boundaries and obstacles were considered, and thn numerical results were compared with those obtained by other methods on standard problems. As a result, it was confirmed that the DO-LBM provides a valuable results in simulating radiative heat transfer in a complex boundary structure, which is simple, accurate and can reduce the computational cost compared to other methods.

In this study, we develop a model for a binary fluid–surfactant system utilizing a coupling of two kinds conservative Allen–Cahn type equations and the Navier–Stokes equations. To ensure mass conservation, we incorporate hybrid Lagrange multipliers into the two Allen–Cahn type equations. Specifically, for the concentration variable, a global correction using a time-dependent Lagrange multiplier is utilized, while for the binary fluid variable, a space–time dependent Lagrange multiplier is applied to minimize the impact of dynamics of motion by mean curvature. We propose a linear second order scheme for practical solution of the model. Computational tests demonstrate that the proposed model is effective for the binary fluid–surfactant system and is capable of preserving the small features of interfaces.

Although non-pharmaceutical interventions such as social distancing have proven effective in curbing outbreaks, they also carry economic consequences. This poses a dilemma for policymakers striving to find a balance between disease control and economic burden. This delicate balance varies regionally, influenced by non-epidemiological factors such as population movements, socio-demographic characteristics, and the intricacies of social distancing policies. These factors interact in intricate ways, shaping the transmission dynamics of COVID-19. To address this complexity, we propose an innovative approach utilizing deep reinforcement learning (RL). This method assists in tailoring intervention policies for diverse regions, taking into account their unique dynamics. We incorporate South Korea’s social distancing policies and their economic impact into a RL framework with a multi-region epidemic model, offering a comprehensive solution. We integrate official mobility data and GDP specific to each region, employing the proximity policy optimization algorithm to determine the most appropriate region-specific social distancing policy. The algorithm’s reward function considers both outbreak control and economic impacts, providing policymakers with the flexibility to fine-tune the balance between these two factors according to their preferences. This adjustment can be performed across three distinct cost scenarios: High, Base, and Low-cost scenarios. In scenarios with High-costs, social distancing measures are aimed at regions with extensive connectivity and higher transmission rates. When costs are moderate, policies center around the period of peak prevalence, illustrating adaptable strategies in areas characterized by high transmission rates, budget limitations, and population mobility. In situations with Low-costs, these measures encompass most regions, excluding those with low transmission rates. The study’s results support focused interventions in specific regions to balance outbreak control and economic impact mitigation.