Journal of Computational and Applied Mathematics最新文献

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.

The potential-free field Schrödinger Cauchy problem is the major topic of this research. Because it is gravely ill-posed in the Hadamard sense. The Cauchy problem is modified through an improved boundary method. The regular approximate solution is created based on the priori and posteriori regularization parameter selection rules, and the convergence evidence is provided. The proposed method is practical under the priori and the posteriori regularization methods, according to numerical experiments. It works well and is resistant to data disruption noise.

In this paper, an optimal decomposition algorithm is introduced to solve a kind of nonlinear fourth-order Emden–Fowler equations (EFEs) that appear in many applied fields. Transforming the Emden–Fowler equation into a Volterra integral equivalent equation allows us to deal with the singularity at the endpoint $x=0$. This conversion also helps to reduce the computational cost of solving the problem. The existence and uniqueness of the solution of each integral equation obtained are established in the corresponding theorems. The convergence analysis further supports the theoretical findings. The accuracy and efficiency of the new method are tested against the existing method (Wazwaz et al., 2014) using numerous cases, and the results show that the presented scheme is a reliable method for computing approximate series solutions and even exact solutions. In addition, the new technique overcomes the drawback of the existing method, that provides only an approximation within a limited interval.

The requirement for high computational efficiency in inversion imaging poses challenges to further enhancing the accuracy of imaging large elastic and viscoelastic models. Considering that forward modeling serves as a prerequisite for inversion imaging, it is essential to introduce a wave propagation simulation method that can enhance simulation accuracy without significantly compromising computational speed. In our paper, cubic B-spline is introduced into the forward modeling of the wave equation. The B-spline collocation method offers a linear complexity for computation and exhibits fourth-order convergence in terms of computational errors. We also find that it can perfectly adapt to the boundary conditions of the perfectly matched layer in the forward modeling solution of the wave simulation. Several typical numerical examples, including 2-D acoustic wave equation, 2-D elastic wave propagation, and 2-D viscoelastic propagation in homogeneous media, are provided to validate its convergence, accuracy, and computational efficiency.