Applied Mathematics Letters最新文献

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Efficient second-order and energy-stable fully discrete scheme for a diffuse-interface tumor growth model 扩散界面肿瘤生长模型的高效二阶能量稳定全离散格式

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-11-17 DOI: 10.1016/j.aml.2025.109825

Guang-an Zou , Yei Xin Zhu , Jing Xiong , Xiaofeng Yang

Tumor growth models based on a Cahn–Hilliard equation coupled with a reaction–diffusion equation for nutrients lead to strongly nonlinear systems, presenting significant challenges for reliable simulation. We develop a fully discrete finite element scheme that is linear, decoupled, second-order accurate in time, and unconditionally energy-stable, achieved through a combination of BDF2 discretization, finite element approximation, and scalar auxiliary variable (SAV) approach. Rigorous analysis establishes unconditional energy stability, while numerical experiments confirm second-order convergence, robustness, and efficiency. Beyond benchmark accuracy and stability tests, the scheme captures complex morphological patterns of tumor growth, including invasive finger-like structures consistent with experimental observations, demonstrating its potential for biologically relevant tumor simulations.

基于Cahn-Hilliard方程和营养物质的反应-扩散方程的肿瘤生长模型导致了强烈的非线性系统，这对可靠的模拟提出了重大挑战。通过BDF2离散化、有限元近似和标量辅助变量（SAV）方法的结合，我们开发了一种线性、解耦、二阶精确和无条件能量稳定的全离散有限元方案。严格的分析建立了无条件的能量稳定性，而数值实验证实了二阶收敛，鲁棒性和效率。除了基准准确性和稳定性测试之外，该方案还捕获了肿瘤生长的复杂形态模式，包括与实验观察一致的侵入性手指样结构，证明了其在生物学相关肿瘤模拟中的潜力。

引用次数: 0

Painlevé integrability, Bäcklund transformation and multi-wave interaction solutions for a generalized (3+1)-dimensional Jimbo–Miwa equation 广义（3+1）维Jimbo-Miwa方程的painlelevel可积性、Bäcklund变换和多波相互作用解

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-11-12 DOI: 10.1016/j.aml.2025.109824

Gui-qiong Xu

This paper investigates the integrability and multi-wave interaction solutions for a generalized (3+1)-dimensional Jimbo–Miwa equation, which describes nonlinear waves in fluid dynamics and plasma physics. By applying the Painlevé analysis and the binary Bell polynomial method, we not only derive the integrability conditions, but also obtain the bilinear form, N-soliton solutions, Bäcklund transformation, and Lax pair. Taking the four-soliton solutions as an example, different choices of parameters yield various multi-wave interactions among kink waves, lumps and breathers, revealing rich interaction phenomena in higher-dimensional nonlinear integrable models.

本文研究了流体力学和等离子体物理中描述非线性波的广义（3+1）维Jimbo-Miwa方程的可积性和多波相互作用解。利用painlevel分析和二元Bell多项式方法，我们不仅得到了可积性的条件，而且得到了双线性形式、n -孤子解、Bäcklund变换和Lax对。以四孤子解为例，不同的参数选择会产生不同的多波相互作用，从而揭示了高维非线性可积模型中丰富的相互作用现象。

引用次数: 0

High-order Gauss–Legendre methods admit a composition representation and a conjugate-symplectic counterpart 高阶高斯-勒让德方法允许一个复合表示和一个共轭辛对应

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-11-08 DOI: 10.1016/j.aml.2025.109823

Felice Iavernaro , Francesca Mazzia , Ernst Hairer

One of the most classical pairs of symplectic and conjugate-symplectic schemes is given by the Midpoint method (the Gauss–Legendre Runge–Kutta method of order 2) and the Trapezoidal rule. These can be interpreted as compositions of the Implicit and Explicit Euler methods, taken in direct and reverse order, respectively. This naturally raises the question of whether a similar composition structure exists for higher-order Gauss–Legendre methods. In this paper, we provide a positive answer by first examining the fourth-order case and then outlining a generalization to higher orders.

由中点法（2阶高斯-勒让德龙格-库塔法）和梯形法则给出了最经典的辛格式和共轭辛格式。这些可以解释为隐式和显式欧拉方法的组合，分别以正序和反序采取。这自然提出了一个问题：高阶高斯-勒让德方法是否存在类似的组合结构？在本文中，我们通过首先检查四阶情况，然后概述到更高阶的推广，提供了一个肯定的答案。

引用次数: 0

An incremental randomized algorithm for singular value decomposition of streaming data matrices 流数据矩阵奇异值分解的增量随机化算法

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-11-06 DOI: 10.1016/j.aml.2025.109822

Yonghe Liu, Fengsheng Wu, Bingxuan Yu, Chaoqian Li

Based on the incremental nature of streaming data and the fast computation of randomized projection algorithms, we propose an incremental randomized algorithm for singular value decomposition (IRSVD) to process streaming data matrices quickly and effectively. The computational complexity of IRSVD is discussed, and the error analysis of IRSVD is provided. Numerical experiments on synthetic data and the recommender system demonstrate the superiority of IRSVD in terms of computational cost.

基于流数据的增量特性和随机化投影算法的快速计算，提出了一种增量随机化奇异值分解（IRSVD）算法来快速有效地处理流数据矩阵。讨论了IRSVD的计算复杂度，并对IRSVD的误差进行了分析。在合成数据和推荐系统上的数值实验证明了IRSVD在计算成本方面的优势。

引用次数: 0

The generalized eigenvalue decomposition of a dual quaternion regular matrix pencil 对偶四元数正则矩阵铅笔的广义特征值分解

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-11-05 DOI: 10.1016/j.aml.2025.109821

Tao Wang , Ying Li , Mingcui Zhang

With the modeling of dual quaternion matrix in multispectral image, it makes multispectral image compression, denoising, blind source separation and other problems possible. In this paper, we study the generalized eigenvalue decomposition of a dual quaternion regular matrix pencil, and present the corresponding computational method by Hermitian and the skew-Hermitian splitting technique and the generalized eigenvalue decomposition of a quaternion regular matrix pencil. Numerical experiment demonstrates the effectiveness of our computational method.

利用对偶四元数矩阵在多光谱图像中的建模，使多光谱图像压缩、去噪、盲源分离等问题成为可能。本文研究了对偶四元数正则矩阵铅笔的广义特征值分解，给出了相应的计算方法——厄米特分割和斜厄米特分裂技术，以及四元数正则矩阵铅笔的广义特征值分解。数值实验证明了计算方法的有效性。

引用次数: 0

A randomized Achlioptas block residual steepest descent method for large sparse overdetermined linear systems 大型稀疏过定线性系统的随机Achlioptas块残差最陡下降方法

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-11-03 DOI: 10.1016/j.aml.2025.109808

Liang Li, Shu-Rong Liu, Tao Li

Clustering is a popular strategy to improve the performance of the randomized block Kaczmarz methods, but it is unavailable for large-scale linear systems due to the substantial complexity associated with clustering high-dimensional data. However, for high-dimensional datasets, the clustering with dimensionality reduction could overcome the aforesaid drawback while achieving comparable clustering results. The Achlioptas random projection, as a powerful dimensionality reduction method, projects high-dimensional data into a low-dimensional space and preserves distance relationships between data points. In this paper, we propose a fast randomized block residual steepest descent method, built upon the Achlioptas random projection and the Gaussian mixture model, for solving large sparse, overdetermined linear systems. The theoretical analysis of which is also established. Numerical experiments are performed to illustrate the effectiveness of the proposed method compared with some existing ones, especially in computing time.

聚类是提高随机块Kaczmarz方法性能的一种流行策略，但由于与高维数据聚类相关的大量复杂性，它不适用于大规模线性系统。然而，对于高维数据集，降维聚类可以克服上述缺点，同时获得可比较的聚类结果。Achlioptas随机投影作为一种强大的降维方法，将高维数据投影到低维空间中，并保持数据点之间的距离关系。在本文中，我们提出了一种基于Achlioptas随机投影和高斯混合模型的快速随机块残差最陡下降方法，用于求解大型稀疏，过确定的线性系统。并对其进行了理论分析。通过数值实验，与现有方法进行了比较，特别是在计算时间方面，验证了该方法的有效性。

引用次数: 0

Scattering below the ground state of odd solutions for the focusing INLS in one dimension 一维聚焦INLS奇解在基态下的散射

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-11-01 DOI: 10.1016/j.aml.2025.109820

Zhi-Yuan Cui, Yuan Li, Dun Zhao

We consider the one-dimensional focusing inhomogeneous nonlinear Schrödinger equation

i \partial_{t} u + Δ u = - {| x |}^{- b} {| u |}^{α} u,

where

0 < b < 1

and

4 - 2 b < α < \infty

. Although this problem has been extensively studied for initial data in

H^{1} (R^{N})

when

N \geq 2

, there were previously no scattering results available for the case

N = 1

due to the singularity introduced by the term

{| x |}^{- b}

. In this paper, by proving a Virial–Morawetz-type estimate for initial data below a certain level, we establish scattering below the ground state with odd initial data in

H^{1} (R)

我们考虑一维聚焦非齐次非线性Schrödinger方程i∂tu+Δu=−|x|−b|u|αu，其中0<；b<；1和4−2b<；α<∞。虽然对于N≥2时H1（RN）的初始数据已经进行了广泛的研究，但由于术语|x|−b引入的奇异性，之前没有得到N=1情况下的散射结果。本文通过对低于一定水平的初始数据证明一个virial - morawetz型估计，建立了H1(R)中初始数据为奇数的基态下散射。

引用次数: 0

Vector nonautonomous nondegenerate soliton solutions in the coupled Gross–Pitaevskii equations 耦合Gross-Pitaevskii方程的矢量非自治非退化孤子解

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-10-30 DOI: 10.1016/j.aml.2025.109804

Jiguang Rao , Lijuan Guo , Jingsong He

This letter investigates vector nonautonomous nondegenerate solitons and their collision dynamics in the coupled Gross–Pitaevskii equations with variable nonlinear coefficients and external potentials. By employing a bilinear representation linked to the KP hierarchy, compact determinant forms of nondegenerate soliton solutions are established. The results reveal several distinct localized waveforms, including single-hump and double-hump solitons, whose propagations follow curved paths dictated by the modulation function

r (t)

. The asymptotic analysis demonstrates two types of collision patterns for double-hump solitons: either retaining their original profiles or undergoing structural transformations. A previously unreported mixed process is also identified, in which one soliton preserves its symmetric profile while the other experiences a symmetry-breaking change. The work provides new insight into controllable nonlinear excitations relevant to vector Bose–Einstein condensates.

本文研究了具有可变非线性系数和外部势的耦合Gross-Pitaevskii方程中的矢量非自治非退化孤子及其碰撞动力学。利用与KP层次相关的双线性表示，建立了非退化孤子解的紧致行列式。结果揭示了几种不同的局域波形，包括单驼峰和双驼峰孤子，其传播遵循由调制函数r(t)决定的弯曲路径。渐近分析证明了双驼峰孤子的两种碰撞模式：要么保持其原始轮廓，要么进行结构转换。还发现了一种以前未报道的混合过程，其中一个孤子保持其对称轮廓，而另一个孤子经历对称破坏变化。这项工作为与矢量玻色-爱因斯坦凝聚相关的可控非线性激励提供了新的见解。

引用次数: 0

A third-order multiscale analysis and computation for the elliptic problem in arbitrarily heterogeneous domains 任意非均质区域椭圆问题的三阶多尺度分析与计算

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-10-30 DOI: 10.1016/j.aml.2025.109806

Qiang Ma , Junzhi Cui

A new third-order multiscale expansion is proposed for the elliptic problem with mixed boundary conditions in arbitrarily heterogeneous domains. The field variable is expanded in terms of a homogenized solution and its derivatives up to the third order. The so-called first to third-order functions are defined to give the homogenized coefficients and correct the differences between the homogenized and original solution both in the domain and on the boundaries. Error estimations are derived, and a typical numerical example is presented demonstrating the high accuracy of the multiscale model. This multiscale analysis presented in this paper generalizes the asymptotic expansion method and can be extended to other problems in non-homogeneous domains.

针对任意非均质域上具有混合边界条件的椭圆型问题，提出了一种新的三阶多尺度展开式。将场变量展开为均质解及其三阶导数的形式。定义了所谓的一阶到三阶函数，以给出均匀化系数，并在定义域和边界上修正均匀化后的解与原解之间的差异。给出了误差估计，并给出了典型的数值算例，证明了多尺度模型具有较高的精度。本文的多尺度分析推广了渐近展开方法，可推广到其他非齐次域的问题。

引用次数: 0

Second-order error analysis for FEM of fractional Laplacian on graded meshes via FDM auxiliary 基于FDM辅助的梯度网格分数阶拉普拉斯有限元二阶误差分析

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-10-30 DOI: 10.1016/j.aml.2025.109807

Jianxing Han , Minghua Chen , Yufeng Nie

On graded meshes, the superlinear convergence for fractional Laplacian problem was proved in Borthagaray et al. (2021) by finite element method (FEM). Furthermore, numerical experiments of FEM in Chen, et al. (2021) demonstrate a second-order accuracy on a suitably graded mesh for the 1D case, but a convergence analysis for the proposed scheme remains unavailable. To fill this gap, we provide a second-order error analysis for the resulting FEM algebraic system. Our analysis employs the finite difference method (FDM) as an auxiliary tool based on our previous work [ arXiv:2520.11117], where FEM scheme can be viewed as a modification of the FDM scheme.

Borthagaray et al.（2021）用有限元法证明了分数阶拉普拉斯问题在梯度网格上的超线性收敛性。此外，Chen等人（2021）的有限元数值实验表明，对于一维情况，在适当的分级网格上具有二阶精度，但对所提出方案的收敛性分析仍然不可用。为了填补这一空白，我们对所得到的有限元代数系统进行了二阶误差分析。我们的分析采用有限差分法（FDM）作为辅助工具，基于我们之前的工作[arXiv:2520.11117]，其中FEM方案可以视为FDM方案的修改。

引用次数: 0

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