Journal of Computational and Applied Mathematics最新文献

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Exact solutions and reductions of nonlinear Schrödinger equations with delay

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-01-01 DOI: 10.1016/j.cam.2024.116477

Andrei D. Polyanin , Nikolay A. Kudryashov

For the first time, Schrödinger equations with cubic and more complex nonlinearities containing the unknown function with constant delay are analyzed. The physical considerations that can lead to the appearance of a delay in such nonlinear equations and mathematical models are expressed. One-dimensional non-symmetry reductions are described, which lead the studied partial differential equations with delay to simpler ordinary differential equations and ordinary differential equations with delay. New exact solutions of the nonlinear Schrödinger equation of the general form with delay, which are expressed in quadratures, are found. To construct exact solutions, a combination of methods of generalized separation of variables and the method of functional constraints are used. Special attention is paid to three equations with cubic nonlinearity, which allow simple solutions in elementary functions, as well as more complex exact solutions with generalized separation of variables. Solutions representing a nonlinear superposition of two traveling waves, the amplitude of which varies periodically in time and space, are constructed. Some more complex nonlinear Schrödinger equations of a general form with variable delay are also studied. The results of this work can be useful for the development and improvement of mathematical models described by nonlinear Schrödinger equations with delay and related functional PDEs, and the obtained exact solutions can be used as test problems intended to assess the accuracy of numerical methods for integrating nonlinear equations of mathematical physics with delay.

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引用次数: 0

Efficient positivity preserving schemes for stochastic complex systems

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-01-01 DOI: 10.1016/j.cam.2024.116464

Can Huang , Huangxin Chen , Qing Cheng , Lijun Chen

We propose a Lagrange multiplier approach for constructing positive preserving scheme for stochastic complex systems. Adopting the approach for deterministic PDEs in Cheng and Shen (2022), we introduce the Karush–Kuhn–Tucker (KKT) condition to enforce positivity. For general stochastic partial complex systems with positive solution, we apply fully implicit schemes. But for stochastic Allen–Cahn equations, the discretization in time is an IMEX tamed Euler scheme and the discretization in space is a spectral Galerkin method with numerical integration, and for stochastic ordinary complex systems, the discretization is a tamed semi-implicit scheme. For all these cases, our schemes are proven to be unconditionally stable. Under regular assumptions for a broad class of SDEs and stochastic Allen–Cahn equation, we are able to provide an optimal strong error analysis. Numerical experiments are provided to validate our theoretical results.

引用次数: 0

A positivity-preserving, second-order energy stable and convergent numerical scheme for a ternary system of macromolecular microsphere composite hydrogels

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-01-01 DOI: 10.1016/j.cam.2024.116463

Lixiu Dong , Cheng Wang , Zhengru Zhang

A second order accurate numerical scheme is proposed and analyzed for the periodic three-component Macromolecular Microsphere Composite(MMC) hydrogels system, a ternary Cahn-Hilliard system with a Flory–Huggins-deGennes free energy potential. This numerical scheme with energy stability is based on the Backward Differentiation Formula(BDF) method in time derivation combining with Douglas-Dupont regularization term, combined the finite difference method in space. We provide a theoretical justification of positivity-preserving property for all the singular terms, i.e., not only the two phase variables are always between 0 and 1, but also the sum of the two phase variables is between 0 and 1, at a point-wise level. In addition, an optimal rate convergence analysis is provided in this paper, in which a higher order asymptotic expansion of the numerical solution, the rough error estimate and refined error estimate techniques have to be included to accomplish such an analysis. This paper will be the first to combine the following theoretical properties for a second order accurate numerical scheme for the ternary MMC system: (i) unique solvability and positivity-preserving property; (ii) energy stability; (iii) and optimal rate convergence. A few numerical results are also presented.

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引用次数: 0

Analysis of a Shear beam model with suspenders in thermoelasticity of type III

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-01-01 DOI: 10.1016/j.cam.2024.116471

Meriem Chabekh , Nadhir Chougui , Delfim F.M. Torres

We conduct an analysis of a one-dimensional linear problem that describes the vibrations of a connected suspension bridge. In this model, the single-span roadbed is represented as a thermoelastic Shear beam without rotary inertia. We incorporate thermal dissipation into the transverse displacement equation, following Green and Naghdi’s theory. Our work demonstrates the existence of a global solution by employing classical Faedo–Galerkin approximations and three a priori estimates. Furthermore, we establish exponential stability through the application of the energy method. For numerical study, we propose a spatial discretization using finite elements and a temporal discretization through an implicit Euler scheme. In doing so, we prove discrete stability properties and a priori error estimates for the discrete problem. To provide a practical dimension to our theoretical findings, we present a set of numerical simulations.

引用次数: 0

Joint state-parameter estimation and inverse problems governed by reaction–advection–diffusion type PDEs with application to biological Keller–Segel equations and pattern formation

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-12-30 DOI: 10.1016/j.cam.2024.116454

Alonzo Flavien , Dia Ben Mansour , Saad Mazen

Inverse problems aim to find the causes of outcoming features knowing the consequences of a model by calibrating the model’s parameters to fit data. In this paper, we present a method that solves simultaneously the inverse problem and the state estimation problem associated with nondegenerate anisotropic reaction–advection–diffusion systems, combined with a smooth observation operator, and showcase it on two examples: a Keller–Segel system used for the chemotaxis, and a Turing system producing stable spatial patterns. The method is defined as an optimization problem that minimizes the misfit formulated with three different types of error: on the modelling choices, on the initial state assumption, and on the difference between data and the forward predictive model output. The resolution of the corresponding inverse problem relies on the rewriting of the variational system and involves solving the forward system while nullifying a vector-valued function that represents the optimality of the coefficients. From a numerical perspective, we approach the inverse problem by adjusting both the state and parameter vectors using sparse temporal data. Instead of employing a classical Newton algorithm, we exploit strategic numerical schemes to effectively handle the resulting coupled system. Numerical experiments in one- and two-dimensional physical domains have been performed with synthetic data to evaluate the efficiency of the proposed method, but also to describe the influence of hyperparameters on the inverse problem.

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引用次数: 0

Hybridizing remora and aquila optimizer with dynamic oppositional learning for structural engineering design problems

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-12-28 DOI: 10.1016/j.cam.2024.116475

Megha Varshney , Pravesh Kumar , Laith Abualigah

To solve global optimization problems, the Aquila Optimizer (AO) algorithm was created recently and is based on the hunting habits of Aquila birds. The Remora Optimization Algorithm (ROA) is combined with a novel Aquila optimizer in this study to create a hybrid version that generates new local solutions based on the best available ones, thereby improving searchability. Additionally, the implementation of dynamic oppositional-based learning (DOL) techniques facilitates both the exploration and exploitation of a search field while preserving an appropriate balance between them. Designated RODAO, is the proposed algorithm. The fundamental characteristic of the proposed approach is the use of Remora's ability to prevent premature convergence and local search problems, as well as the DOL strategy to preserve high-quality solutions and variety among the RODAO's solutions. In order to assess these competencies in RODAO, the IEEE CEC 2017 benchmark functions as well as a traditional set of well-known benchmark functions have been used. The robustness and efficiency of the method are guaranteed by a number of performance measurements used on RODAO, including statistical tests and convergence graphs. Three popular engineering optimization issues are also solved in the paper using the suggested RODAO technique. The analysis and numerical experiments show that real-world optimization issues can be successfully solved by the proposed algorithm or RODAO.

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引用次数: 0

Reliability analysis of imperfect repair and switching failures: A Bayesian inference and Monte Carlo simulation approach

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-12-27 DOI: 10.1016/j.cam.2024.116458

Chandra Shekhar , Mahendra Devanda , Keshav Sharma

Reliability analysis of complex systems is essential to ensuring their dependable operation. This study examines a dual-active, single-standby storage unit system, which is integral to various industrial and technological applications. The research delves into the reliability metrics of this system, particularly addressing the challenges posed by unreliable repairs and standby switching failures. Bayesian inference, utilizing Gamma and Beta prior distributions along with Monte Carlo simulations, offers a robust methodology for estimating unknown parameters and deriving posterior distributions. The analysis assumes exponential distributions for both time-to-failure and time-to-repair, while time-to-inspection for perfect and imperfect rejuvenations also follows exponential distributions. The probability of unsuccessful standby switching, denoted as

q

, is incorporated into the model. The results, presented through detailed tables and graphical representations, provide valuable insights into the system’s reliability and the effectiveness of the statistical methods employed.

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引用次数: 0

Two hybrid conjugate gradient based algorithms on Riemannian manifolds with adaptive restart strategy for nonconvex optimization problems

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-12-27 DOI: 10.1016/j.cam.2024.116452

Meixuan Jiang , Yun Wang , Hu Shao , Ting Wu , Weiwei Sun

In this paper, we propose two hybrid conjugate gradient algorithms for solving nonconvex optimization problems on Riemannian manifolds. The conjugate parameter of the first method extends a hybrid formula [Comput. Oper. Res. 159 (2023) 106341] from Euclidean to Riemannian spaces. The conjugate parameter of the second method integrates the Fletcher–Reeves conjugate parameter with another flexible conjugate parameter. An adaptive restart strategy is then incorporated into their respective search directions to enhance their theoretical properties and computational efficiency. As a result, both methods independently generate sufficient descent directions regardless of any stepsize strategy on Riemannian manifolds. Under typical assumptions and using the Riemannian weak Wolfe conditions to generate stepsize, the global convergence results of these two families are demonstrated. Numerical comparisons with existing methods using different Riemannian optimization scenarios verify the effectiveness of our proposed methods.

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引用次数: 0

Non-fragile sampled-data control for uncertain fractional-order systems with time-varying delay

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-12-26 DOI: 10.1016/j.cam.2024.116438

Lianglin Xiong , Junzhou Dai , Haiyang Zhang

The aim of this paper is to investigate a novel fractional order integral inequality (FOII) for reducing the conservatism of the stability and the non-fragile sampled-data control (NFSDC) criterion for the uncertain fractional-order systems (FOSs) with time-varying delay (TVD). Firstly, in order to estimate the quadratic derivative of fractional-order integral more accurately, a new FOII with free weighting matrix is proposed, which has a tighter upper bound than the existing FOII. Second, in order to more accurately reflect the delay variation and reduce the data transmission frequency, the influence of uncertainty and time-varying delay are considered, the NFSDC scheme followed by the discussed stability criterion is given based on our novel piecewise Lyapunov functional and introduced FOII. Finally, three numerical examples demonstrate the feasibility and superiority of the proposed method.

引用次数: 0

Two explicit methods for one-sided Lipschitz stochastic differential equations driven by fractional Brownian motion

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-12-26 DOI: 10.1016/j.cam.2024.116462

Jingjun Zhao, Hao Zhou, Yang Xu

For solving the stochastic differential equations with the one-sided Lipschitz and polynomial increasing drift coefficients driven by fractional Brownian motion, we propose the tamed Euler–Maruyama method and the explicit Euler–Maruyama method with projection. By using the modified coefficients, the errors of these two explicit methods are analyzed recursively and the convergence rates are obtained. A numerical experiment is carried out to support our theoretical results.

引用次数: 0

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