Journal of Applied Mathematics and Computing最新文献

This article introduces a Haar wavelet-based numerical method for solving fifth-order linear and nonlinear differential equations. This method easily handles both homogeneous and nonhomogeneous equations. It also works with variable and constant coefficients under various conditions. The method is flexible, making it easy to work with boundary, integral, and two-point integral conditions. These three different cases of given information are coupled with fifth-order linear and nonlinear differential equations, and the method proves to be effective in these cases. The outcomes of the Haar wavelet collocation technique are compared with approaches found in existing literature. The method demonstrates second-order convergence, and experimental results support this idea as well. The CPU time is used to evaluate the efficiency of the method, and the maximum absolute errors ((L_infty )) are utilized to assess the accuracy level. Different examples are studied along with various given information, and the method is found to be adaptable to different types of boundary conditions and particular integral conditions.

We formulate a stochastic differential equation(SDE) model from a deterministic model of imperfect vaccination building on a recent analytical approach of We suggest it appears as Allen et al [5] 81(2):487-515, 2020. https://doi.org/10.1007/s00285-020-01516-8), which derivation procedure is based on the elementary events occurring during the epidemiological dynamics and their corresponding probabilities. We prove the global existence of a unique weak non-negative solution starting from the non-negative initial value of the formulated model. We compute the conditions under which extinction and persistence in mean hold, and illustrate our theoretical results using numerical simulations. Determining the stochastic outcome of epidemiological dynamics under imperfect vaccination is important to optimize vaccination campaigns.

It has been shown that the effectiveness of some algorithms involving permutation code equivalence depends on hulls of linear codes. This paper focuses on studying ternary linear one-dimensional hull codes, and further considers the largest minimum distance (d_1(n, k)) among all ternary linear one-dimensional hull [n, k] codes for (nle 20) or (k le 3). Most importantly, we classify optimal ternary linear one-dimensional hull [n, 2] codes. Further, we construct some ternary linear one-dimensional hull codes with better minimum distances compared with known results.

This paper estimates the lower bound for the enclosure of the smallest singular value of interval matrices. Different lower bounds are derived using specific inequalities and interval matrix norms. Relation between some of these lower bounds is studied. The theoretical results are verified through a numerical example.

We consider a hierarchically structured population in which the amount of resources an individual has access to is affected by individuals that are larger, and that the intake of resources by an individual only affects directly the growth rate of the individual. We formulate a deterministic model, which takes the form of a delay equation for the population birth rate. We also formulate an individual based stochastic model, and study the relationship between the two models. In particular the stationary birth rate of the deterministic model is compared to that of the quasi-stationary birth rate of the stochastic model. Since the quasi-stationary birth rate cannot be obtained explicitly, we derive a formula to approximate it. We show that the stationary birth rate of the deterministic model can be obtained as the large population limit of the quasi-stationary birth rate of the stochastic model. This relation suggests that the deterministic model is a good approximation of the stochastic model when the number of individuals is sufficiently large.

In this research article, we introduce an investigation for analytical approximate solutions of the time-fractional nonlinear shallow water model. This model is described as a system of coupled partial differential equations that characterize the dynamics of water motion below a pressure surface in oceanic or sea environments, which is distinguished by the fact that the vertical dimension is smaller in magnitude than the typical horizontal dimension. The modified generalized Mittag-Leffler function method is an effective and innovative analytical technique to acquire convenient approximate solutions for this fractional order model. The methodology of proposed method to solve general fractional nonlinear partial differential equations is presented. Also, the convergence of this method and estimated error analysis for the projected solutions are proved. The approximate solutions gained by our method when (alpha =1) are compared with the recognized exact solutions and outcomes of other techniques in the same conditions published in the literature, including the residual power series method, natural transform decomposition method, modified homotopy analysis transform method and new iterative method. Moreover, some two and three-dimensional graphs and tabulated data display a simulation of acquired results. Also, the influence of (alpha ) on the behavior of solutions is exhibited. The findings demonstrate the effectiveness and advantages of the suggested method, including not requiring any linearization or perturbation and transformations, easily computable components, implemented directly to the problems, satisfactory approximate solutions and a small absolute error.

In this paper, we use direct algebra and improved generalized Riccati equation methods to investigate optical soliton solutions to the Chavy-Waddy-Kolokolnikov model for bacterial colonies. The model is effective at phototaxis, which is the generation of bacterial aggregates that move toward the light. The model’s solitary wave solutions are obtained using the direct algebra and Ricatti equation methods, which take into account the minor perturbations of the linear case as well as the regimes of pattern generation and instability. For each case, we determined the dynamic of optical soliton solutions for the model, which includes hyperbolic, periodic soliton solutions for the linear case and stationary spike-like solutions for the nonlinear case. The methods produced several types of hyperbolic, periodic, and exponential solutions for this model that were not previously specified in the literature. We also presented the 2D and 3D graphs to show the kink, bright, and dark solitary wave structures with suitable numerical values. The obtained solutions will be of great importance in chemotaxis and phototaxis bacterial adaptations.

Let G be a graph with n vertices, and ({d_{i}}) be the degree of its i-th vertex. The ABS matrix of G is the square matrix of order n whose (i, j)-entry is equal to ({sqrt{({d_{i}+d_{j}-2})/({d_{i}+d_{j}})}}) if the i-th vertex and the j-th vertex of G are adjacent, and 0 otherwise. Let (rho _1ge rho _2ge cdots ge rho _{n}) be the eigenvalues of the ABS matrix of G. Then the ABS Estrada index of G, denoted by (E_{ABS}(G)), is defined as (E_{ABS}(G)=sum _{i=1}^{n}e^{rho _i}). In this paper, the chemical importance of the ABS Estrada index is investigated and it is shown that the predictive ability of ABS Estrada index is stronger than other connectivity Estrada indices (including Randić Estrada index, harmonic Estrada index and ABC Estrada index) and ABS index for octane isomers. Since chemical graphs of octane isomers are trees, we study the extremal problem of ABS Estrada index of trees, and prove that for any tree (T_n) with (nge 3) vertices,

with equality in the left (resp., right) inequality if and only if (T_n) is isomorphic to the path (P_n) (resp., the star (K_{1,n-1})).