Computational and Applied Mathematics最新文献

In this paper, we propose an error analysis of fully decoupled time-discrete scheme for the Cahn–Hilliard-MHD (CHMHD) diffuse interface model. Firstly, we use the “zero-energy-contribution" technique to reconstruct the system by introducing three scalar auxiliary variables (SAV). Secondly, we construct first-order semi-discrete SAV scheme for this new system by using pressure-correction method, and we also demonstrate its unconditional stability in energy. Then, we give a detailed implementation procedure to show that the proposed scheme is linear and fully decoupled, and only a series of elliptic equations with constant coefficients need to be solved at each time step. Moreover, we establish the optimal convergence rate by rigorous error analysis. Finally, we present numerical experiments to validate the accuracy, stability and efficiency of the proposed scheme.

In recent years, tensor problems have been studied in multiple fields of science and engineering including applied mathematics, the theory of completely integrable quantum, data mining, statistics, physics, chemistry, machine learning, medical engineering, and others. In machine learning, the word tensor informally refers to two different concepts that organize and represent data. In this work, at first, the concept of the sign function of a tensor is developed using the sign function of a matrix. Then, we propose an iterative method to find the sign function of a tensor. We prove that the order of convergence of the proposed method is three. Finally, we extend the iterative method for solving the Young–Baxter equation, which has many applications in fully integrable quantum theory, classical systems, and exactly solvable models of statistical physics. The accuracy and effectiveness of the proposed method in comparison to well-known methods are demonstrated by various numerical examples.

The aim of this paper is to introduce a new two-step inertial method for approximating a solution to a generalized split common fixed point problem, which is a unique solution to a variational inequality problem. We establish a strong convergence theorem for the sequence generated by the algorithm. We explore various special cases related to fundamental problems, including the split feasibility problem, the split common null point problem, and the constrained convex minimization problem. To demonstrate the efficacy and performance of our proposed algorithm, we apply it to a practical scenario involving support vector machines for binary classification. The algorithm is employed on diverse datasets sourced from the UC Irvine Machine Learning Repository, serving as the training set.

This paper investigates the existence of Eberlein weakly almost periodic solutions for differential equations of the form (u'=Au+f(t)) and (u'=A(t)u+f(t)). In the first scenario, when A generates a strongly asymptotically semigroup, we establish the existence of Eberlein-weakly almost periodic solutions, thereby extending and improving a previous result in Zaidman(Ann Univ Ferrara 14(1): 29–34, 1969). In the second case, we consider a more general situation where A(t) is a (possibly nonlinear) operator satisfying a monotony condition. Unlike most existing works in the literature, our approach does not rely on tools of exponential dichotomy and Lipschitz nonlinearity. Lastly, we illustrate the practical relevance of our findings by presenting real-world models, including a hematopoiesis model, that exemplify the key findings. A numerical simulation is also provided.

The relationship is studied here between the 3D incompressible Brinkman–Forchheimer problem with delay and its generalized steady state. First, with some restrictive condition on the delay term, the global well-posedness of 3D Brinkman–Forchheimer problem and its steady state problem are obtained by compactness method and Brouwer fixed point method respectively. Then the global (textbf{L}^{p}~ (2le p<infty )) decay estimates are established for weak solution of non-autonomous Brinkman–Forchheimer equations with delay by using a retarded integral inequality. The global decay estimates can be proved for strong solution as well. Finally, the exponential stability property is investigated for weak solution of the 3D non-autonomous Brinkman–Forchheimer problem by a direct approach and also for the autonomous system by using a retarded integral inequality. Furthermore, the Razumikhin approach is utilized to achieve the asymptotic stability for strong solution of autonomous system under a relaxed restriction.

In this paper, we analyze the stability and Hopf bifurcation of the fractional-order logistic equation with two different delays (tau _{1}, tau _{2}>0): (D^{alpha }y(t)=rho y(t-tau _{1})left( 1-y(t-tau _{2})right) ), (t>0), (rho >0). We describe stability regions by using critical curves. We explore how the fractional order (alpha ), (rho ), and time delays influence the stability and Hopf bifurcation of the model. Then, by choosing (rho ), fractional order (alpha ), and time delays as bifurcation parameters, the existence of Hopf bifurcation is studied. An Adams-type predictor–corrector method is extended to solve fractional-order differential equations involving two different delays. Finally, numerical simulations are given to illustrate the effectiveness and feasibility of theoretical results.

The study of the existence of finitely many chaotic attractors in the Chua’s system is a classical topic. In this article, a class of generalized Chua’s systems is introduced, where the nonlinear items are extended by a type of polynomial functions. The existence of infinitely many chaotic attractors is studied, which can not be observed in the classical Chua’s system. A lot of interesting dynamical behavior can be obtained in this kind of systems under certain conditions: (i) the coexistence of infinitely many self-excited attractors; (ii) the existence of multi-scroll attractors as well as strange dynamics with growing-scroll, where growing-scroll refers to the number of the scrolls of the attractors is increasing as time is increasing; (iii) the coexistence of infinitely many hidden attractors. Furthermore, the circuit simulations for two examples from this kind of generalized Chua’s systems illustrate the possible existence of infinitely many hidden and multi-scroll attractors under certain conditions.

This article explores various techniques for generating fractal-like Bézier curves in both 2D and 3D environments. It delves into methods such as subdivision schemes, Iterated Function System (IFS) theory, perturbation of Bézier curves, and perturbation of Bézier basis functions. The article outlines conditions on subdivision matrices necessary for convergence and demonstrates their use in creating an IFS with an attractor aligned to the convergent point of the subdivision scheme based on specified initial data. Additionally, it discusses conditions for obtaining a one-sided approximation of a given Bézier curve through perturbation. The article also addresses considerations for perturbed Bézier basis functions to construct fractal-like Bézier curves that remain within the convex hull polygon/polyhedron defined by control points. These methods find applications in various fields, including computer graphics, art, and design.

In this article, we first convert a second order singularly perturbed boundary value problem (SPBVP) into a pair of initial value problems, which are solved later using exponential time differencing (ETD) Runge–Kutta methods. The stability analysis of the proposed scheme is addressed. Some linear and non-linear problems have been solved to study the applicability of the proposed method.

In this paper, we extend the Chen and Moore determinants of quaternion Hermitian matrices to dual quaternion Hermitian matrices. We show the Chen determinant of dual quaternion Hermitian matrices is invariant under addition, switching, multiplication, and unitary operations at the both hand sides. We then show the Chen and Moore determinants of dual quaternion Hermitian matrices are equal to each other, and they are also equal to the products of eigenvalues. The characteristic polynomial of a dual quaternion Hermitian matrix is also studied.