Computational and Applied Mathematics最新文献

The study presented in this paper consists of a grouping of methods for determining numerical solutions to the Poisson equation (heat diffusion) with high accuracy. We compare the results obtained with classical second-order finite difference method (CDS-2) with fourth-order compact (CCDS-4) and the exponential methods (EXP-4). We accelerate the convergence of the numerical solutions using the geometric multigrid method and then apply the completed Richardson extrapolation (CRE) across the full temperature field. This proposed clustering determined solutions with two orders of accuracy higher for all three methods presented in the study, in addition to recommending the EXP-4 method together with CRE for its accuracy and low computational effort. The evidence for our results was established through qualitative verification, through the assessment of orders of accuracy of the discretization error; and quantitative verification, through the analysis of CPU time and complexity order of the numerical solutions calculated. The numerical solutions of sixth-order of accuracy obtained after proposed CRE methodology using the CCDS-4 and EXP-4 methods are recognized as benchmark solutions for these two classes of methods.

This paper is devoted to the study of Lagrange synchronization of nonidentical discrete-time fractional-order quaternion-valued neural networks (DFQNNs) with time delays. First, a new inequality is established by using the definition and operational principles of quaternion sign function. Next, in order to achieve Lagrange synchronization, a state feedback controller is designed. And then, some criteria are derived to guarantee Lagrange synchronization of nonidentical DFQNNs by employing Lyapunov method and fractional difference theory as well as quaternion properties. Finally, the validity and feasibility of the theoretical results are verified by numerical simulations.

The phenomenological Landau–Lifshitz equation (LL) suggested by Landau and Lifshitz in 1935 to describe the precessional motion of spins in ferromagnetic materials has shown its limitations when the temperature is close to or above the Curie temperature. This model has been replaced by the Landau–Lifshitz–Bloch model (LLB), which proves its efficiency in modelling magnetic phenomena at all temperature ranges. In this work, we propose an implicit finite element scheme for the latter model. We show that the proposed scheme converges to a weak solution of the (LLB) equation. In practice, a nonlinear system must be solved at each step of time. So, we use a fixed point method to solve this system. Finally, some numerical experiments have been given to show the performance of our approach.

Given a graph (G=(V,E)), the Perfect Italian domination function is a mapping (f:Vrightarrow {0,1,2}) such that for any vertex (vin V) with f(v) equals zero, (sum _{uin N(v)}f(u)) must be two. In simpler terms, for each vertex v labeled zero, one of the following conditions must be satisfied: (1) exactly two neighbours of v are labeled 1, and every other neighbour of v is labeled zero, (2) exactly one neighbour of v is labeled 2, and every other neighbour of v is labeled zero. The weight of the function f is calculated as the sum of f(u) over all (uin V). The Perfect Italian domination problem involves finding a Perfect Italian domination function that minimizes the weight. We have devised a linear-time algorithm to solve this problem for (P_4)-sparse graphs, which represent well-established generalization of cographs. Furthermore, we have proved that the problem is efficiently solvable for distance-hereditary graphs. We have also shown that the decision version of the problem is NP-complete for 5-regular graphs and comb convex bipartite graphs.

In this paper, we have focused on a multi-objective fractional semi-infinite programming problems in which the constraints and objective functions are tangentially convex. A result has been established to find the tangential subdifferential of a fractional function, assuming the numerator and the negative of the denominator being tangentially convex functions. With this, optimality conditions have been derived using a non-parametric approach under (digamma )-convexity assumption. Further, a Mond–Weir type dual has been considered and weak and strong duality relations have been developed. Moreover, an application in robot trajectory planning has been considered and solved using MATLAB. In addition, considering the same trajectory as in Vaz et al. (Eur J Oper Res 153(3):607–617, 2004), we have compared the results obtained in MATLAB with the results available in Vaz et al. (Eur J Oper Res 153(3):607–617, 2004) and Haaren-Retagne (A semi-infinite programming algorithm for robot trajectory planning, 1992), where the authors have solved using AMPL. It has been observed that our results are more efficient than the previously available results, with the implementation of MATLAB as it substantially reduces the computational time. Throughout the paper, nontrivial examples have also been provided for proper justification of the theorems developed.

Nonnegative matrix factorization (NMF) is a popular dimensionality reduction technique. NMF is typically cast as a non-convex optimization problem solved via standard iterative schemes, such as coordinate descent methods. Hence the choice of the initialization for the variables is crucial as it will influence the factorization quality and the convergence speed. Different strategies have been proposed in the literature, the most popular ones rely on singular value decomposition (SVD). In particular, Atif et al. (Pattern Recognit Lett 122:53–59, 2019) have introduced a very efficient SVD-based initialization, namely NNSVD-LRC, that overcomes the drawbacks of previous methods, namely, it guarantees that (i) the error decreases as the factorization rank increases, (ii) the initial factors are sparse, and (iii) the computational cost is low. In this paper, we improve upon NNSVD-LRC by using the low-rank structure of the residual matrix; this allows us to obtain NMF initializations with similar quality to NNSVD-LRC (in terms of error and sparsity) while reducing the computational load. We evaluate our proposed solution over other NMF initializations on several real dense and sparse datasets.

This paper explores quasi-synchronization for a class of fractional-order complex-valued BAM neural networks (FCBAMNNs) with time delays, discontinuous activation functions, and uncertainties. Firstly, by utilizing Laplace transform and the Mittag–Leffler function property, a novel fractional differential inequality is derived. Then, sufficient conditions are obtained to ensure the quasi-synchronization for the considered FCBAMNNs by means of non-decomposable method. Additionally, the error bound of synchronization is explicitly evaluated. Finally, a numerical example is provided to validate the proposed results.

This paper addresses the challenge of solving Fokker–Planck equations, which are prevalent mathematical models across a myriad of scientific fields. Due to factors like fractional-order derivatives and non-linearities, obtaining exact solutions to this problem can be complex. To overcome these challenges, our framework first discretizes the given equation using the Crank-Nicolson finite difference method, transforming it into a system of ordinary differential equations. Here, the approximation of time dynamics is done using forward difference or an L1 discretization technique for integer or fractional-order derivatives, respectively. Subsequently, these ordinary differential equations are solved using a novel strategy based on a kernel-based machine learning algorithm, named collocation least-squares support vector regression. The effectiveness of the proposed approach is demonstrated through multiple numerical experiments, highlighting its accuracy and efficiency. This performance establishes its potential as a valuable tool for tackling Fokker–Planck equations in diverse applications.

We present new iterative algorithms for solving a split convex feasibility problem with multiple output sets involving a monotone mixed variational inequality in real Hilbert spaces. The proposed algorithms follow the Tseng projection method, but with self-adaptive step-sizes that do not depend on the norm of the transfer operator as well as knowledge of a Lipschitz constant. The convergence of the sequences generated by the proposed algorithms is established. We use the proposed algorithms to solve a modified oligopolistic Nash–Cournot equilibrium model. Numerical experiments show that our algorithms are efficient and competitive compared to several recent algorithms.

In this paper we consider single-machine scheduling problems with group technology, where the group setup times are general linear functions of their starting times and the jobs in the same group have general truncated learning effects. The objective is to minimize the makespan and total completion time, respectively. We show that the makespan minimization remains polynomially solvable. For the total completion time minimization, optimal properties are presented and then we introduce some heuristic algorithms and a branch-and-bound algorithm.