Applied Mathematics Letters最新文献

For block-oriented Hammerstein systems with a static nonlinear part and a dynamic linear part, there exists a problem of the parameter coupling in nonlinear part and linear part. Traditional methods are to express its output into a linear or a quasi linear regression equation about parameters. However, a Hammerstein system with a neural network (NN) nonlinear part is difficult to be expressed as a linear regression equation about weights and parameters. This paper decomposes parameter coupling by substituting the nonlinear NN equation into the separated key-term of the linear part through the key-term separation idea, and casts the system model into three fictitious models through the hierarchical decomposition principle. Then a hierarchical gradient algorithm is adopted to alternatively identify parameters of these three models. The advantages of the presented Hammerstein system are of the mapping ability of NNs, and the memory ability of dynamic models.

In this letter, we further investigate the Hermitian symmetric space derivative nonlinear Schrödinger equation through the development of a semi-degenerate Darboux transformation. To demonstrate the utility of this approach, we first reveal the expression of the double-periodic wave solution. On the periodic background, we visualize the kink-breather wave, the rogue wave and their interaction.

This paper introduces a fast direct algorithm for the singular boundary method (SBM) in two-dimensional (2D) problems, utilizing the hierarchical off-diagonal low-rank (HODLR) matrix concept as the foundation of the fast direct solver. The HODLR matrix is constructed by hierarchically partitioning the coefficient matrix into blocks using a binary tree, with all off-diagonal blocks at each level being represented as low-rank factors. Furthermore, The Sherman-Morrison-Woodbury formula can be used to efficiently compute the inverse of the HODLR matrix. The numerical experiment results demonstrate that the new fast solver can significantly improve the computational efficiency of the SBM while maintaining the same level of precision.

This paper is devoted to the computation of the approximate $K$-term t-SVD of third-order tensors via random techniques. With a given truncated term $K$, we obtain the two-side randomized algorithms for the approximate $K$-term t-SVD, denoted by two-sided randomized t-SVD. Furthermore, we delve into the deterministic and probabilistic error bounds, considering specific presumptions regarding the proposed algorithm. Additionally, we integrate the current algorithm with the power method to enhance the precision of the approximate $K$-term t-SVD. To demonstrate the effectiveness of our proposed algorithm, we present several numerical examples.

In this paper, the (3+1)-dimensional defocusing Gardner-KP equation is investigated again with the help of Lie symmetry method since the results are either incorrect, or incomplete, or misleading in the literature. For the Lie algebra of infinitesimal symmetries spanned by eight vector fields, the one-dimensional optimal system of subalgebra is established by leveraging the fundamental invariants and general adjoint transformation representation. Meanwhile, by virtue of some infinitesimal generators in the optimal system, several symmetry reductions and exact solutions are presented.

In this paper, a meshless generalized finite difference method (GFDM) is proposed to solve the time fractional diffusion-wave (TFDW) equations. A second-order temporal discretization scheme is developed to tackle the Caputo fractional derivative, and then spatial discretization formulas are derived by the GFDM. Theoretical accuracy and convergence of the GFDM for TFDW equations are analyzed. Numerical results verify the theoretical results and the efficiency of the method.

Cooperative hunting can increase the predator’s hunting ability. In this work, we study a stochastic eco-epidemiological predator–prey model incorporating hunting cooperation. By constructing appropriate auxiliary functions, we establish a sufficient criterion for the existence of a unique ergodic stationary distribution. The findings imply that cooperative hunting has a significant effect on the density of infected predators when the epidemic is protracted.

In this paper, a two-parameter singularly perturbed problem with discontinuous source and convection coefficient is studied. This problem is discretized by using a first-order upwind finite difference scheme for which a posteriori error analysis in the maximum norm is derived. Then, based on this a posteriori error estimation, a grid iteration algorithm is designed to generate an adaptive nonuniform mesh. Finally, Numerical experiments are proposed to confirm that our proposed method is first-order uniformly convergent.

We carry out an analysis of the existence of solutions for a class of nonlinear fractional partial differential equations of parabolic type with nonlocal initial conditions. Sufficient conditions for the solvability of the desired problem are presented by transforming it into an abstract non-autonomous fractional evolution equation, and constructing two families of solution operators based on the Mittag-Leffler function, the Mainardi Wright-type function and the analytic semigroup generated by the closed densely defined operator $-A\left(\cdot \right)$. The discussions are based on the fractional power theory as well as the Banach fixed point theorem in the interpolation space $X_p^{\upsilon }$ ($0⩽\upsilon <1$, $1<p<\infty$).

In this paper, we consider the global well-posedness of the 3D damped micropolar Bénard system with horizontal dissipation. Global existence and uniqueness of the solution of system (1.1) are proved for $\beta \ge 4$ and $\alpha >0$.