Computational and Applied Mathematics最新文献

In this paper, we address some of the computational challenges associated with the RMIL+ conjugate gradient parameter by proposing an efficient conjugate gradient (CG) parameter along with its generalization to the Riemannian manifold. This parameter ensures the good convergence properties of the CG method in Riemannian optimization and it is formed by combining the structures of two classical CG methods. The extension utilizes the concepts of retraction and vector transport to establish sufficient descent property for the method via strong Wolfe line search conditions. Additionally, the scheme achieves global convergence using the scaled version of the Ring-Wirth nonexpansive condition. Finally, numerical experiments are conducted to validate the scheme’s effectiveness. We consider both unconstrained Euclidean optimization test problems and Riemannian optimization problems. The results reveal that the performance of the proposed method is significantly influenced by the choice of line search in both Euclidean and Riemannian optimizations.

In the present work, we construct a sixth order derivative free family without memory for solving nonlinear operator equations in Banach spaces. We further modify this to a ninth order family with memory without any additional functional evaluation. Local convergence analysis of both these methods have been studied using assumptions only on the first derivative. Numerical computations validate the theoretical results and show the superiority of our methods over the existing ones. Basins of attraction have also been presented to see the dynamical behaviour of the proposed methods.

This paper studies the common variational inclusion problem in real Hilbert spaces. To solve this problem, we propose a new accelerated approach with two initial parameter steps and establish a strong convergence theorem. Our scheme combines the viscosity approximation method with Tseng’s forward backward-forward splitting method and uses self-adaptive step sizes. We simultaneously compute the inertial extrapolation and viscosity approximation at the first step of each iteration. We show that the iterative method converges strongly under conventional and appropriate assumptions. We also study some applications to the common minimum point problems, split feasibility problems, and to the least absolute selection and shrinkage operators (LASSO). Finally, we present two numerical results in Hilbert space and an application to the LASSO problem in order to illustrate the convergence analysis of the considered methods as well as compare our results to the related ones introduced by Cholamjiak et al. (J. Sci. Comput., 88(85), 2021) and Gibali and Thong (Calcolo, 55(49), 2018).

In this paper, Chebyshev polynomial derivative-based spectral schemes are constricted for solving linear and non-linear ordinary differential equations. Linearization relation and some essential integrated formulae concerning the basis functions are provided to deal with the spectral tau method. Unlike the regular weight function, another modified weight is introduced. Also, different patterns and results have been obtained regarding the relation between the Jacobi polynomials, ultraspherical polynomials, Chebyshev polynomials, and their derivatives. Moreover, the algebraic systems of the spectral expansion for solving the Riccati, Lane–Emden equations, and water contamination model are discussed. Error bounds are introduced, studied, and proven. Finally, several real applications are numerically solved using 2ndDCh polynomial-based spectral tau method. The obtained results are compared with different methods to confirm the accuracy and efficiency of the schemes.

Competition graphs, which are mathematical representations of competitive relationships among entities, have found applications in various domains. This article introduces and explores several types of graphs, including fuzzy incidence competition graphs, fuzzy incidence neighborhood graphs, p-competition fuzzy incidence graphs, m-step fuzzy incidence competition graphs, and m-step fuzzy incidence neighborhood graphs. We establish sufficient conditions under which an edge is independent strong or independent incidence strong. Relation between competition graphs of isomorphic fuzzy incidence digraphs is established. Through rigorous analysis, several intriguing results concerning these graphs are derived. Additionally, at the end of the article, we evaluate a group of researchers using fuzzy incidence graphs to identify the most influential member within the group.

This article is concerned with the problem of source identification for a distributed-order time-fractional diffusion equation (DTFDE). The uniqueness, ill-posedness and conditional stability estimate for the inverse source problem are demonstrated. Our main objective is to reconstruct the stable source term utilizing an iterative generalized quasi-reversibility method(IGQRM). In theory, an a priori and an a posteriori regularization parameter selection strategies are proposed to obtain the convergence estimates between the regularized solution and the exact solution. In numerical experiment, some numerical examples are presented to describe the stability and validity of our proposed regularization method.

In this paper we apply a methodology introduced in Navarro Jimenez et al. (J Chem Phys 145(24):244106, 2016) in the framework of chemical reaction networks to perform a global sensitivity analysis on simulations of a continuous-time Markov chain model motivated by epidemiology. Our goal is to quantify not only the effects of uncertain parameters such as epidemic parameters (transmission rate, mean sojourn duration in compartments), but also those of intrinsic randomness and interactions between epidemic parameters and intrinsic randomness. For that purpose, following what was proposed in Navarro Jimenez et al. (2016), we leverage three exact simulation algorithms for continuous-time Markov chains from the state of the art which we combine with common tools from variance-based sensitivity analysis as introduced in Sobol’ (Math Model Comput Exp 1:407–414, 1993). Also, we discuss the impact of the choice of the simulation algorithm used for the simulations on the results of sensitivity analysis. Such a discussion is new, at least to our knowledge. In a numerical section, we implement and compare three sensitivity analyses based on simulations obtained from different exact simulation algorithms of a SARS-CoV-2 epidemic model.

This paper introduces the (Psi )-formable integral transform, discusses the several essential properties and results—Convolution, (Psi )-formable transform of tth derivative, (Psi )-Riemann Liouville fractional integration and differentiation, (Psi )-Caputo fractional differentiation, (Psi )-Hilfer fractional differentiation, (Psi )-Prabhakar fractional integration and differentiation, and (Psi )-Hilfer–Prabhakar fractional derivatives. Next, we use the Fourier integral and (Psi )-Modifiable conversions to solve some Cauchy-type fractional differential equations using the generalized three-parameter Mittag–Leffler function and (Psi )-Hilfer–Prabhakar fractional derivatives.

Let (dot{G}) be a signed graph and (A(dot{G})) be its adjacency matrix. The eigenvalues of (dot{G}) are actually the eigenvalues of (A(dot{G})), and the girth of (dot{G}) is the length of a shortest cycle in (dot{G}). We use (mathscr {B}(n,g)) to denote the set of unbalanced signed bicyclic graphs on n vertices with girth g. In this paper, we focus on the least eigenvalues of signed graphs in (mathscr {B}(n,g)) and accordingly determine the extremal signed graph which achieves the minimal least eigenvalue.

In this work, we present the modelling and numerical simulation of a molten glass fluid flow in a furnace melting basin. We first derive a model for a molten glass fluid flow and present numerical simulations based on the finite element method (FEM). We further discuss and validate the results obtained from the simulations by comparing them with experimental results. Finally, we also present a non-intrusive proper orthogonal decomposition (POD) based on artificial neural networks (ANN) to efficiently handle scenarios which require multiple simulations of the fluid flow upon changing parameters of relevant industrial interest. This approach lets us obtain solutions of a complex 3D model, with good accuracy with respect to the FEM solution, yet with negligible associated computational times.