Journal of Applied Mathematics and Computing最新文献

We propose a forward–backward splitting dynamical system for solving inclusion problems of the form (0in A(x)+B(x)) in Hilbert spaces, where A is a maximal operator and B is a single-valued operator. Involved operators are assumed to satisfy a generalized monotonicity condition, which is weaker than the standard monotone assumptions. Under mild conditions on parameters, we establish the fixed-time stability of the proposed dynamical system. In addition, we consider an explicit forward Euler discretization of the dynamical system leading to a new forward backward algorithm for which we present the convergence analysis. Applications to other optimization problems such as constrained optimization problems, mixed variational inequalities, and variational inequalities are presented and some numerical examples are given to illustrate the theoretical results.

The main goal of this document is to demonstrate the existence of a unique solution and determine the computational solution of the Quadratic mixed integral equation of Volterra Fredholm type (QMIE) of (2 + 1) dimensional in the space ({L}_{2}([0,a]times [0,b])times C[0,T],(T<1).) Banach’s fixed-point hypothesis describes questions regarding the existence of the solution as well as its uniqueness. Furthermore, we discuss the convergence of the solution and the stability of the numerical solution’s error. QMIE ultimately results in a set of Quadratic integral equations in position when the quadratic numerical approach is used. Then, using the orthogonal polynomial technique while applying the Jacobi polynomial method, we obtain a nonlinear algebraic system of equations. Several illustrative examples in numerical form are shown below to explain the procedures and all the numerical outcomes are calculated and the corresponding errors are computed according to the Maple 18 program.

In linear coding theory, self-dual cyclic codes are especially notable for their efficiency in both encoding and decoding processes. This research focuses on the enumeration of such codes over finite fields, denoted as ({mathbb {F}}_q), where (q = 2^m) and m is the field size. Traditionally, investigations in this area have faced significant constraints primarily due to two factors. The first is the length of the code, n, with a focus on excluding prime factors congruent to 1 modulo 8. The second limitation pertains to the binary case, specifically when (m = 1). To overcome these challenges, this study introduces the concept of the exact power character of 2, a novel approach that offers a significant methodological advancement. By reframing the existing numerical constraints in terms of three readily computable parameters, this approach effectively sidesteps the limitations previously existing in the field. This development not only broadens the scope of possible code lengths and field sizes but also enhances the potential for practical applications of self-dual cyclic codes in various areas of information theory and communications.

In this paper, based on the weighted alternating direction implicit method, we investigate a second-order scheme with variable steps for the two-dimensional time-fractional telegraph equation (TFTE). Firstly, we derive a coupled system of the original equation by the symmetric fractional-order reduction (SFOR) method. Then the renowned L2-(1_sigma ) formula on graded meshes is employed to approximate the Caputo derivative and a weighted ADI scheme for the coupled problem is constructed. In addition, with the aid of the Grönwall inequality, the unconditional stability and convergence of the weighted ADI scheme are analyzed. Finally, the numerical experiments are shown to verify the effectiveness and correctness of theoretical results.

This article analyzes stability issues of positive switched homogeneous systems (PSHSs) including partial unstable subsystems. The quasi-time-dependent max-separable Lyapunov function is firstly constructed to investigate exponential stability problems for PSHSs with unstable subsystems under mode dependent average dwell time switching rule, which not only covers the previous conclusions but also reduces conservatism in comparison to time-independent results. Besides, stability conditions are accessed conveniently by handling a nonlinear programming. Finally, this paper puts forward a numerical example to illustrate the credibility of findings.

In this paper, we investigate a general delayed diffusive predator–prey system with taxis and fear effect, which can have different functional response functions. By selecting the taxis coefficient and the discrete time delay as bifurcation parameters, we first derive an algorithm for calculating the third-order truncated normal form of Turing-Hopf bifurcation for this system. To demonstrate the effectiveness of the derived algorithm, we investigate a delayed diffusive predator–prey system with taxis, fear effect, and square root functional response function. We employ stability theory and bifurcation theory to study the existence of codimension-two Turing-Hopf bifurcation and obtain the third-order truncated normal form of Turing-Hopf bifurcation using the derived algorithm. With the obtained third-order truncated normal form of Turing-Hopf bifurcation for this practical system, we can analytically determine the dynamical classifications near the Turing-Hopf bifurcation point. Finally, we perform numerical simulations to verify the theoretical analysis results.

The problem of assessing and prioritizing various economic systems and their types from the perspective of decision-making is a complex problem, which involves the evaluation of multiple conflicting criteria in the presence of uncertainty and incomplete information. The imprecisions of fuzzy set theory and the existing decision-making (DM) approaches could not fully take into account the complexities and subtleties that are embedded in this problem. Hence, the need to create a better DM model that can handle both the bipolar and complex nature of the economy and come up with a more comprehensive and robust solution. Thus, in this manuscript, we devise a DM technique in the setting of the bipolar complex fuzzy set (BCFS). For this, we firstly investigate various generalized Maclaurin symmetric mean operators in the setting of BCFS that are bipolar complex fuzzy generalized Maclaurin symmetric mean, bipolar complex fuzzy weighted generalized Maclaurin symmetric mean, bipolar complex fuzzy generalized geometric Maclaurin symmetric mean, and bipolar complex fuzzy weighted generalized geometric Maclaurin symmetric mean operators. After that, we use a newly developed decision-making technique in the context of economic systems and find that the traditional economic system is the finest economic system. In the last, we compare the developed work with a certain number of prevailing theories to reveal the supremacy and advantages. The proposed work.

In this work, we consider boundary value problems with characteristic, non-characteristic, and two mixed lines of type change for a fractionally loaded equation. The equation under consideration is a loaded parabolic-hyperbolic type with a fractional integral operator, where the hyperbolic part is a characteristic load. By assuming the load is characteristic under necessary conditions on the given functions, we prove the unique solvability of the resulting integral equations derived from the formulated problems. Consequently, the problems also have unique solutions.

In this paper, we consider a modified Levenberg–Marquardt algorithm for Low Order Value Optimization problems(LOVO). In the algorithm, we obtain the search direction by a combination of LM steps and approximate LM steps, and solve the subproblems therein by QR decomposition or cholesky decomposition. We prove the global convergence of the algorithm theoretically and discuss the worst-case complexity of the algorithm. Numerical results show that the algorithm in this paper is superior in terms of number of iterations and computation time compared to both LM-LOVO and GN-LOVO algorithm.

We are focused on the numerical treatment of a singularly perturbed degenerate parabolic convection–diffusion problem that exhibits a parabolic boundary layer. The discretization and analysis of the problem are done in two steps. In the first step, we discretize in time and prove its uniform convergence using an auxiliary problem. In the second step, we discretize in space using an upwind scheme on a Bakhvalov-type mesh and prove its uniform convergence using the truncation error and barrier function approach, wherein several bounds derived for the mesh step sizes are used. Numerical results for a couple of examples are presented to support the theoretical bounds derived in the paper.