Article
Mathematics, Applied
Jianfeng Liu, Tingchun Wang, Teng Zhang
Summary: This paper presents a linearized second-order finite difference scheme for solving the nonlinear time-fractional Schrodinger equation. The optimal error estimate of the numerical solution is established under a weak assumption on the nonlinearity, without any restriction on the grid ratio. The analysis employs mathematical induction method, several inverse Sobolev inequalities, and a discrete fractional Gronwall-type inequality. The proposed scheme exhibits a convergence rate of O(tau(2) + h(2)) with time step tau and mesh size h.
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics, Applied
Mohamed Rahmeni, Khaled Omrani
Summary: This paper considers a high-order finite difference method for the two-dimensional coupled nonlinear Schrodinger equations. The method is proven to preserve the total mass and energy in a discrete sense and an optimal error estimate is established using the standard energy method. Numerical results are compared with exact solutions and other existing methods, showing improved accuracy in both spatial and temporal directions.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Computer Science, Interdisciplinary Applications
Yu. I. Dimitrienko, Shuguang Li, Yi Niu
Summary: In this paper, the numerical simulation of the generalized Rosenau-RLW equation is studied using a compact finite difference method, leading to a discrete scheme that maintains the conservative properties of the equation. Good numerical stability and convergence are achieved, with numerical experiment results confirming the accuracy and efficiency of the method.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Mathematics, Applied
Xin Li, Hong-lin Liao, Luming Zhang
Summary: A fast compact difference scheme is presented for simulating subdiffusion problems, achieving computational efficiency and rigorous stability and error estimates. Three numerical experiments confirm the effectiveness of the proposed algorithm.
NUMERICAL ALGORITHMS
(2021)
Article
Mathematics, Applied
Samira Labidi, Khaled Omrani
Summary: This paper investigates a high-order finite difference scheme for the nonlinear Schrodinger equation with wave operator, showing the existence of solutions using a variant of Brouwer fixed point theorem, discussing the stability and uniqueness of the difference scheme, and ultimately proving the convergence of the scheme through the energy method.
APPLIED NUMERICAL MATHEMATICS
(2022)
Article
Mathematics, Applied
Kejia Pan, Jiali Zeng, Dongdong He, Saiyan Zhang
Summary: This paper proposes an efficient semi-implicit difference scheme for solving the fractional nonlinear Schrodinger equation with wave operator. The scheme is fourth-order accurate in space, second-order accurate in time, unconditionally stable, and has been rigorously proven to have unique solvability, unconditional stability, and convergence in the-norm. Numerical experiments are conducted to confirm the theoretical results.
APPLICABLE ANALYSIS
(2022)
Article
Computer Science, Interdisciplinary Applications
Dingwen Deng, Qiang Wu
Summary: This paper investigates the numerical solutions of the nonlinear couple wave equations using the combination of compact difference method, Predictor-Corrector iterative methods, and Richardson extrapolation methods. The proposed methods are proven to be stable, convergent, and efficient through theoretical analysis and numerical experiments.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Mathematics, Applied
Qing Li, Huanzhen Chen
Summary: This article proposes a compact difference method for fractional viscoelastic beam vibration in stress-displacement form. The solvability, unconditional stability, and convergence rates of the stress v and displacement u are rigorously proved. Numerical experiments are conducted to verify the theoretical findings. The main contribution of this article is evaluating the lower and upper bounds of the eigenvalues of the Toeplitz matrix Lambda generated from the weighted Grunwald difference operator, improving the existing semi-positive definiteness theory of the matrix Lambda for fractional differential operators, and facilitating the proof of stability and convergence for the stress v. (C) 2022 Elsevier Inc. All rights reserved.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Interdisciplinary Applications
Ren Liu, Xiaozhong Yang, Peng Lyu
Summary: A parallelized computation method for inhomogeneous time-fractional Fisher equation is proposed in this paper. The method shows high precision and distinct parallel computing characteristics, and its unique existence, unconditional stability, and convergence are theoretically proved.
FRACTAL AND FRACTIONAL
(2022)
Article
Computer Science, Interdisciplinary Applications
Kanyuta Poochinapan, Ben Wongsaijai
Summary: This paper introduces weighted parameters in standard compact difference operators and applies high-order compact finite difference operators and the Crank-Nicolson/Adams-Bashforth method to solve coupled BBM equations. The numerical results demonstrate that the proposed weighted compact finite difference scheme can improve computational efficiency and numerical accuracy.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Mathematics, Applied
Hanen Boujlida, Kaouther Ismail, Khaled Omrani
Summary: This study investigates a high-order accuracy finite difference scheme for solving the one-dimensional extended Fisher-Kolmogorov (EFK) equation. A new compact difference scheme is proposed and the a priori estimates and unique solvability are discussed using the discrete energy method. The unconditional stability and convergence of the difference solution are proved. Numerical experiments demonstrate the accuracy and efficiency of the proposed technique.
APPLIED NUMERICAL MATHEMATICS
(2024)
Article
Mathematics, Applied
Gengen Zhang, Chunmei Su
Summary: This paper introduces a highly accurate conservative method for solving the quantum Zakharov system, which is fourth-order accurate in space and second-order accurate in time according to detailed numerical analysis. The proposed scheme's conservation properties and high accuracy are confirmed through various numerical examples. Additionally, the compact scheme is used to study the convergence rate of the quantum Zakharov system to its limiting model in the semi-classical limit.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Mathematics
Denis Ivanovich Borisov, Dmitry Mikhailovich Polyakov
Summary: We consider general higher-order matrix elliptic differential-difference operators with small variable translations. Operators are introduced by general higher-order quadratic forms on arbitrary domains. Our main results show that the considered operators converge to ones with zero translations in the best operator norm, and estimates for the convergence rates are established. We also prove the convergence of the spectra and pseudospectra.
Article
Mathematics, Applied
Emadidin Gahalla Mohmed Elmahdi, Sadia Arshad, Jianfei Huang
Summary: In this paper, a linearized compact difference scheme for one-dimensional time-space fractional nonlinear diffusion-wave equations with initial boundary value conditions is proposed. The initial singularity of the solution is considered and the Crank-Nicolson technique, combined with other formulas, is used for time and spatial discretization. The proposed scheme is shown to have unconditional stability, convergence, and high accuracy in both time and space through theoretical analysis and numerical experiments.
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
(2023)
Article
Mathematics, Applied
Qing Li, Huanzhen Chen, Hong Wang
Summary: In this article, a proper orthogonal decomposition-compact difference scheme (POD-CDS) is proposed for the displacement-stress form of a simply supported plate vibration model. It is proven that the POD-CDS can maintain the same spatial and temporal convergence rates and unconditional stability as the compact difference solution, while significantly improving computing efficiency. Stability and convergence analysis for the corresponding compact difference scheme is also conducted. Numerical experiments verify the theoretical findings and demonstrate that the POD-CDS is nearly 10-30 times faster than the compact difference scheme.
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics, Applied
Peter Frolkovic, Nikola Gajdosova
Summary: This paper presents compact semi-implicit finite difference schemes for solving advection problems using level set methods. Through numerical tests and stability analysis, the accuracy and stability of the proposed schemes are verified.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Md. Rajib Arefin, Jun Tanimoto
Summary: Human behaviors are strongly influenced by social norms, and this study shows that injunctive social norms can lead to bi-stability in evolutionary games. Different games exhibit different outcomes, with some showing the possibility of coexistence or a stable equilibrium.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Dingyi Du, Chunhong Fu, Qingxiang Xu
Summary: A correction and improvement are made on a recent joint work by the second and third authors. An optimal perturbation bound is also clarified for certain 2 x 2 Hermitian matrices.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Pingrui Zhang, Xiaoyun Jiang, Junqing Jia
Summary: In this study, improved uniform error bounds are developed for the long-time dynamics of the nonlinear space fractional Dirac equation in two dimensions. The equation is discretized in time using the Strang splitting method and in space using the Fourier pseudospectral method. The major local truncation error of the numerical methods is established, and improved uniform error estimates are rigorously demonstrated for the semi-discrete scheme and full-discretization. Numerical investigations are presented to verify the error bounds and illustrate the long-time dynamical behaviors of the equation with honeycomb lattice potentials.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kuan Zou, Wenchen Han, Lan Zhang, Changwei Huang
Summary: This research extends the spatial PGG on hypergraphs and allows cooperators to allocate investments unevenly. The results show that allocating more resources to profitable groups can effectively promote cooperation. Additionally, a moderate negative value of investment preference leads to the lowest level of cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kui Du
Summary: This article introduces two new regularized randomized iterative algorithms for finding solutions with certain structures of a linear system ABx = b. Compared to other randomized iterative algorithms, these new algorithms can find sparse solutions and have better performance.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Shadi Malek Bagomghaleh, Saeed Pishbin, Gholamhossein Gholami
Summary: This study combines the concept of vanishing delay arguments with a linear system of integral-algebraic equations (IAEs) for the first time. The piecewise collocation scheme is used to numerically solve the Hessenberg type IAEs system with vanishing delays. Well-established results regarding regularity, existence, uniqueness, and convergence of the solution are presented. Two test problems are studied to verify the theoretical achievements in practice.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Qi Hu, Tao Jin, Yulian Jiang, Xingwen Liu
Summary: Public supervision plays an important role in guiding and influencing individual behavior. This study proposes a reputation incentives mechanism with public supervision, where each player has the authority to evaluate others. Numerical simulations show that reputation provides positive incentives for cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Werner M. Seiler, Matthias Seiss
Summary: This article proposes a geometric approach for the numerical integration of (systems of) quasi-linear differential equations with singular initial and boundary value problems. It transforms the original problem into computing the unstable manifold at a stationary point of an associated vector field, allowing efficient and robust solutions. Additionally, the shooting method is employed for boundary value problems. Examples of (generalized) Lane-Emden equations and the Thomas-Fermi equation are discussed.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Lisandro A. Raviola, Mariano F. De Leo
Summary: We evaluated the performance of novel numerical methods for solving one-dimensional nonlinear fractional dispersive and dissipative evolution equations and showed that the proposed methods are effective in terms of accuracy and computational cost. They can be applied to both irreversible models and dissipative solitons, offering a promising alternative for solving a wide range of evolutionary partial differential equations.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Yong Wang, Jie Zhong, Qinyao Pan, Ning Li
Summary: This paper studies the set stability of Boolean networks using the semi-tensor product of matrices. It introduces an index-vector and an algorithm to verify and achieve set stability, and proposes a hybrid pinning control technique to reduce computational complexity. The issue of synchronization is also discussed, and simulations are presented to demonstrate the effectiveness of the results obtained.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Ling Cheng, Sirui Zhang, Yingchun Wang
Summary: This paper considers the optimal capacity allocation problem of integrated energy systems (IESs) with power-gas systems for clean energy consumption. It establishes power-gas network models with equality and inequality constraints, and designs a novel full distributed cooperative optimal regulation scheme to tackle this problem. A distributed projection operator is developed to handle the inequality constraints in IESs. The simulation demonstrates the effectiveness of the distributed optimization approach.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Abdurrahim Toktas, Ugur Erkan, Suo Gao, Chanil Pak
Summary: This study proposes a novel image encryption scheme based on the Bessel map, which ensures the security and randomness of the ciphered images through the chaotic characteristics and complexity of the Bessel map.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Xinjie Fu, Jinrong Wang
Summary: In this paper, we establish an SAIQR epidemic network model and explore the global stability of the disease in both disease-free and endemic equilibria. We also consider the control of epidemic transmission through non-instantaneous impulsive vaccination and demonstrate the sustainability of the model. Finally, we validate the results through numerical simulations using a scale-free network.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Maria Han Veiga, Lorenzo Micalizzi, Davide Torlo
Summary: The paper focuses on the iterative discretization of weak formulations in the context of ODE problems. Several strategies to improve the accuracy of the method are proposed, and the method is combined with a Deferred Correction framework to introduce efficient p-adaptive modifications. Analytical and numerical results demonstrate the stability and computational efficiency of the modified methods.
APPLIED MATHEMATICS AND COMPUTATION
(2024)