Journal of Computational and Applied Mathematics最新文献

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.

Developing modern computer technologies makes it possible not only to solve complex computing problems, but also gives rise to new problems of optimal usage of computing resources. Modern computers can use multiple processors simultaneously and dynamically change the speed of calculations due to additional energy consumption for performing intensive calculations. We consider the speed scaling scheduling problem with energy constraint and parallel jobs. The total sum of completion times is minimized. The NP-hardness of the problem is proved and a mixed integer convex program with continuous time representation is proposed. For searching near-optimal solutions in quick time we develop a genetic algorithm with the generational replacement scheme. The genetic algorithm is experimentally tested and compared with the known greedy algorithm and local improvements technique on meaningful instances. The numerical results highlight the effectiveness and the efficiency of the proposed algorithm. The lower bounds on the objective function and convex program are also experimentally evaluated.

In this paper we consider three-state $k$-out-of-$n$ system composed of components which lifetimes are modeled by independent and identically distributed discrete random variables. The primary focus is the random vector representing the numbers of components in each state. We derive its joint distribution. For illustration, we provide examples of the systems with components with geometrically distributed lifetimes following the Markov degradation process.

The control net of tensor product Bézier-Smart surfaces of arbitrary degree is characterized. Moreover, it is shown that for any given pair of Bézier curves with the same midpoint there always exists a family of Bézier-Smart surfaces with these diagonal curves. We give a method to generate BS-surfaces starting from different sets of user prescribed information, such as diagonal curves or boundary data.

In this paper, we extend the modulus-based matrix splitting method for solving the vertical nonlinear complementarity problem. Some necessary convergence conditions of the proposed methods are investigated. Numerical examples are given to compare with the existing methods. These results can be extended for solving general complementarity problems.

In this paper, we study a heat transfer scenario in Darcy–Forchheimer porous media with variable density. The block-centered finite difference method is applied to discretize the non-isothermal flow equations governing the system. Specifically, the pressure field is modeled using the nonlinear Darcy–Forchheimer formulation, while the density and temperature are described by convection-dominated diffusion equations, which are treated via the characteristic method. Theoretical analyses are rigorously developed for pressure, velocity, density, temperature, and auxiliary flux across non-uniform grids. Several numerical experiments are carried out to illustrate the merits of our method by comparing numerical results to analytical solutions.

The purpose of this paper is to construct a newly efficient finite element method which named as modified finite element method, for Maxwell’s equation in Kerr-type nonlinear media. Because the efficient unconditional stable alternative direction implicit method can’t extend to the Maxwell’s equations in Kerr-type nonlinear media (the difficulty will be discussed in section 3.1), we design the modified method to construct an efficient unconditional stable scheme for Maxwell’s equations in Kerr-type nonlinear media. Furthermore, combined with the direct method, we construct a more efficient direct modified scheme. Comparisons of the efficiency, stability, convergence rate for our modified method and classical explicit leapfrog method were done by theoretical analysis and numerical experiments. The modified method is unconditional stable and its efficiency is not less than leapfrog method.

In this article, the problem of seeking fixed points for global operators over the time-varying graphs in a real Hilbert space is studied. The global operator is a linear combination of local operators, each local operator being accessed privately by one agent for less resource consumption. All agents form a network and they need to cooperate to solve problems. To this end, on the basis of the centralized Ishikawa iteration, the distributed Ishikawa algorithm (D-I) is first proposed. In the sequel, to predigest the calculational complexity, further considering the situation that only the random part of each operator coordinate is calculated in each iteration, the distributed block coordinate Ishikawa algorithm (D-BI) is also designed. The results indicate that the proposed D-I and D-BI algorithms can weakly converge to a fixed point of the multi-agent global operator. Eventually, we give a few numerical examples to illustrate practical benefits of the proposed algorithms.