Applied Mathematics Letters最新文献

We derive a class of space homogeneous Landau-like equations from stochastic interacting particles. Through the use of relative entropy, we obtain quantitative bounds on the distance between the solution of the N-particle Liouville equation and the tensorised solution of the limiting Landau-like equation.

New oscillatory criteria are established for the second-order linear advanced differential equation. Riccati’s technique and suitable estimates of non-oscillatory solutions are used for the proof of the results obtained. The presented criteria, in a certain sense, generalize the known ones.

In this note, we extend the analysis for the residual-based a posteriori error estimators in the energy norm defined for the algebraic flux correction (AFC) schemes (Jha, 2021) to the newly proposed algebraic stabilization schemes (John and Knobloch, 2022; Knobloch, 2023). Numerical simulations on adaptively refined grids are performed in two dimensions showing the higher efficiency of an algebraic stabilization with similar accuracy compared with an AFC scheme.

A Leslie–Gower predator–prey model with square root response function and generalist predator is considered, and the existence and stability of equilibria of the system are discussed. It is shown that the system undergoes a degenerate Hopf bifurcation of codimension exactly two, where there exist two limit cycles. In addition, we find that the system has a cusp of codimension two and exhibits a Bogdanov–Takens bifurcation of codimension two. Our results reveal richer dynamics than the system with no generalist predator.

The construction and analysis of structure-preserving finite element method (FEM) for computing the perturbed wave equation of quantum mechanics are demonstrated. Firstly, a new fully discrete system is built and proved conservative in the sense of the energy. Meanwhile, the boundedness of the numerical solution is derived. Secondly, the existence and uniqueness of the solution are obtained with the help of the Brouwer fixed-point theorem and some special splitting technique. Thirdly, we provide a comprehensive superclose analysis, offering the global superconvergent result. Finally, numerical results are presented to illustrate the theoretical analysis.

To better explore the dynamics of pests, this paper deals with a brand-new predator–pest model with diffusion and additional food. The existence and diffusion-driven Turing instability of positive constant solutions are discussed. We obtain that for additional food of a certain quality and quantity, there exists a critical value such that the model can produce four forms of positive constant solutions as the predation rate of predators is greater than the critical value, and only one form of positive constant solution as the predation rate is less than the critical value. For predator–pest model, which is a new finding indeed. Meanwhile, we conclude that the introduction of diffusion can lead to Turing instability of positive constant solutions. This indicates that the model is likely to produce spatial pattern with certain conditions.

This paper is devoted to a chemotaxis system with signal-dependent motility under homogeneous Neumann boundary conditions in a bounded domain. We prove that this problem possesses a global classical solution which is uniformly bounded under weaker conditions than that obtained by Lv and Wang (2020). The findings of our study demonstrate the presence of a consistent decay rate, effectively ruling out the occurrence of blow-up phenomena in the system across all spatial dimensions.

Noisy tensor recovery aims to estimate underlying low-rank tensors from the noisy observations. Besides the sparse noise, tensor data can also be corrupted by the small dense noise. Existing methods typically use the Frobenius norm to handle the small dense noise. In this work, we build a new nonconvex model to decompose the low-rank and sparse components. To be specific, we employ the ${\ell }_1$ norm to handle the small dense noise term, the ${\ell }_0$ ‘norm’ to enforce the sparse outliers, and the tensor nuclear norm to model the underlying low-rank tensor. We develop an effective alternating minimization-based algorithm. Under certain conditions, we prove that the proposed method has a high probability of exactly recovering low-rank and sparse tensors. Numerical experiments showcase the advantage of our method.

In this paper an extension of the Adaptive Antoulas-Anderson (AAA) Model Order Reduction (MOR) method to time-domain data is defined, referred to as Time-Domain AAA (TDAAA). Inspired by other rational approximation time-domain MOR methods, like Time-Domain Vector Fitting (TDVF) and Time-Domain Loewner Framework (TDLF), TDAAA combines the adaptivity and flexibility of the AAA method in the frequency domain with an error minimization in the time domain. This combination makes the method an interesting alternative to fully time-domain or frequency-domain MOR methods. A combination of AAA and TDVF is also proposed, called AAA-TDVF, where the initial TDVF poles are selected by AAA. This new poles initialization improves both accuracy and convergence speed. Both TDAAA and TDVF are discussed in detail and their performance is compared on a benchmark LTI system.

The Flux Reconstruction (FR) method is classically used in the Computational Fluid Dynamics field. However, its use for the simulation of electromagnetic wave propagation is not as developed yet. Following on from the development of a priori error estimates for the 1D wave equations, we introduce optimisation problems to allow an adaptation of the FR correction polynomial functions to the discretisation parameters. Showing notable accuracy gains in 1D, especially in the preasymptotic regime, we generalise this procedure to the 3D Maxwell’s equations, leading to similar interesting possibilities to reduce the computational cost for a given accuracy.