Journal of Computational and Applied Mathematics最新文献

In this work, the penalty method is studied for the mixed Stokes–Darcy problem, motivated by the penalty method applied to Stokes equation. This work first proposes the penalty Stokes–Darcy model at the continuous level. Then we prove that the solution of the penalty model converges strongly to the original solution as $O\left(ϵ\right)$ in which the penalty parameter is $ϵ\to 0$. What is more, the finite element method is used to solve the penalty model and the optimal error estimates are presented. Finally, several numerical tests are carried out to verify our theoretical results.

The problem of determining the existence of Nash equilibria in $n$-person nonzero-sum generalized differential games is highly intricate and constrained by the advancement of partial differential equations theory. There is limited existing research literature on this subject. This paper presents an existence theorem for open-loop Nash equilibria employing the Fan-Glicksberg fixed point theorem. The $n$-person nonzero-sum bounded rationality generalized differential game model is formulated by introducing a bounded rationality function, and its structural stability and robustness are studied. The conclusions indicate that in the sense of Baire classification, most $n$-person nonzero-sum bounded rationality generalized differential games are structurally stable and robust in the set of $\varepsilon$-open-loop Nash equilibria, and we can approximate the equilibrium set obtained with full rationality generalized differential games by the ${\varepsilon }^k$-open-loop Nash equilibria set obtained with bounded rationality generalized differential games.

This paper investigates the time-consistent reinsurance and investment strategies for insurers based on the alpha-robust mean–variance criterion. We assume that transaction costs with quadratic form exist in the financial market composed of a risk-free asset and $n$ risky assets, and the insurance and financial markets are correlated. By solving a system of extended HJB equations, the equilibrium reinsurance and investment strategy and the corresponding value function are derived in terms of the solution to a system of matrix Riccati equations. In some special cases, more explicit expressions for the equilibrium strategies and value functions are provided. Numerical examples demonstrate that the growth rate of investment slows down as the transaction costs level or the correlation coefficient increases. In addition, we find that the transaction costs level has opposite effects on the utility losses due to ignoring jumps or ambiguity.

The aim of this paper is to derive a refined first-order expansion formula in $R^n$, the goal being to get an optimal reduced remainder, compared to the one obtained by usual Taylor’s formula. For a given function, the formula we derived is obtained by introducing a linear combination of the first derivatives, computed at $n+1$ equally spaced points. We show how this formula can be applied to two important applications: the interpolation error and the finite elements error estimates. In both cases, we illustrate under which conditions a significant improvement of the errors can be obtained, namely how the use of the refined expansion can reduce the upper bound of error estimates.

This paper introduces a numerical approach for the practical solution of the modified Fisher–Kolmogorov–Petrovsky–Piskunov equation that describes population dynamics. The diffusion term and nonlinear term is based on the operator splitting method and interpolation method, respectively. The analytic proof of the discrete maximum principle and positivity preserving for the numerical algorithm is demonstrated. Numerical solution calculated using the proposed method remains stable without blowing up, which implies that the proposed method is unconditionally stable. Numerical studies show that the proposed method is second-order convergence in space and first-order convergence in time. The performance and applicability of the proposed scheme are studied through various computational tests that present the effects of model parameters and evolution dynamics.

Climate variability affects the changes in controlling diseases transferred by insects. An increase in the population, the growth of communities, and a lack of public health infrastructure bring about the return of diseases of which insects are carriers, one of the illness issues. Therefore, the disease control is significant to help reduce the burden on the government and strengthen the country's public health structure. This research proposes a novel approach to modeling dengue fever dynamics, we employ a fractional derivative model with the Atangana–Baleanu–Caputo derivative, which offers a more accurate representation of real-world disease dynamics compared to traditional integer-order models. Basic qualifications are proposed. Equilibrium points and basic reproduction numbers are analyzed. The next-generation matrix method is used to identify the transmission. Besides, parameter sensitivity analysis is performed to learn about factors affecting input parameter values' effects on the basic reproduction number. It was found that the most common parameter affecting the transmission was the biting rate of mosquitoes was 1. In addition, the existence and uniqueness of the solution are examined using the Banach fixed point theorem. The Toufik–Atangana method is used for the numerical examination of a fractional version of the proposed model. We compared different values of fractional-order α=0.965, 0.975, 0.985, 0.995 and 1 it was found that when the order of derivatives decreases, the transmission shall decrease accordingly. This research provides valuable insights for developing effective control strategies to reduce the burden of dengue fever and strengthen public health systems.

Kokol and Stopar (2023) recently studied the exact region ${\Omega }_{\varphi ,\rho }$ determined by Spearman’s footrule $\varphi$ and Spearman’s $\rho$ and derived a sharp lower, as well as a non-sharp upper bound for $\rho$ given $\varphi$. Considering that the proofs for establishing these inequalities are novel and interesting, but technically quite involved we here provide alternative simpler proofs mainly building upon shuffles, symmetry, denseness and mass shifting. As a by-product of these proofs we derive several additional results on shuffle rearrangements and the interplay between diagonal copulas and shuffles which are of independent interest. Moreover we finally show that we can get closer to the (non-sharp) upper bound than established in the literature so far.

We investigate fractional Peano kernels for continuous linear functionals, in the context of differintegral operators with Mittag-Leffler kernel. New bounds for polynomial interpolation are obtained and numerical computations are shown, indicating improvements.

This paper investigates the pricing of exchange options under hybrid models integrating stochastic volatility and stochastic interest rates. It aims to achieve two primary objectives. First, we derive a closed-form pricing formula for exchange options under a two-factor Heston–Hull–White hybrid model, which accounts for long-term volatility and exhibits relatively broad correlations among the dynamics of asset prices, volatilities, and interest rates. Second, we explore the Heston model’s integration with a generalized single-factor stochastic interest rate model, illustrating that the price is not dependent on the specific form of the interest rate process. A closed-form pricing formula for exchange options under this framework is also derived. Our numerical experiments support the proposed formulas and elucidate the effects of various parameters on option prices.