Article
Mathematics, Applied
Tongxin Yan, Changfeng Ma
Summary: This work presents an iterative algorithm for solving a class of generalized coupled Sylvester-conjugate matrix equations over generalized Hamiltonian matrices. It is shown that a generalized Hamiltonian solution can be obtained within finite iteration steps in the absence of round-off errors if the equations are consistent. By choosing special initial matrices, the minimum-norm solution can be obtained, and numerical examples demonstrate the effectiveness of the iterative algorithm.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Multidisciplinary Sciences
Jing Jiang, Ning Li
Summary: In this paper, an iterative algorithm is proposed for solving the generalized (P, Q)-reflexive solution group of quaternion matrix equations. The algorithm can derive the generalized (P, Q)-reflexive solution group and the least Frobenius norm generalized (P, Q)-reflexive solution group by choosing appropriate initial matrices. Moreover, the optimal approximate generalized (P, Q)-reflexive solution group to a given matrix group can be obtained by computing the least Frobenius norm generalized (P, Q)-reflexive solution group of a reestablished system of matrix equations. Numerical examples are provided to illustrate the effectiveness of the algorithm.
Article
Mathematics
Dussadee Somjaiwang, Parinya Sa Ngiamsunthorn
Summary: This paper studies the existence and monotone iterative approximation of mild solutions of fractional-order neutral differential equations involving a generalized fractional derivative. The existence of mild solutions is obtained via fixed point techniques in a partially ordered space. The approach is constructive and can be applied numerically, and an example is provided to demonstrate the convergence of a monotone sequence of functions to a solution.
JOURNAL OF MATHEMATICS
(2022)
Article
Acoustics
Naglaa M. El-Shazly, Mohamed A. Ramadan, Marwa H. El-Sharway
Summary: This paper establishes two relaxed gradient-based iterative algorithms for solving the generalized Sylvester-conjugate matrix equation. Numerical tests are conducted to demonstrate the effectiveness of the proposed approaches.
JOURNAL OF VIBRATION AND CONTROL
(2022)
Article
Materials Science, Multidisciplinary
Florian Herz, Svend-Age Biehs
Summary: This article introduces a many-body theory for thermal far-field emission of dipolar dielectric and metallic nanoparticles in the vicinity of a substrate within the framework of fluctuational electrodynamics. The theoretical model includes the definition of temperatures for each nanoparticle, the substrate temperature, and the temperature of the background thermal radiation separately. The versatility of the method is demonstrated by discussing the thermal radiation of SiC and Ag nanoparticles above a planar SiC and Ag substrate. The results obtained using the discrete dipole approximation are also discussed.
Article
Physics, Fluids & Plasmas
Uday Singh, Ankit Raina, V. K. Chandrasekar, D. Senthilkumar
Summary: This study uncovers the collective dynamics of two coupled nonlinearly damped Lienard oscillators, focusing on the emergence of a nontrivial amplitude death state and quasiperiodic attractors. Analytical critical curves are deduced to explain the stability regions of the nontrivial fixed point and the neutrally stable trivial steady state, matching simulation boundaries. The dynamics also show multistability and a reemergence of states with changes in coupling strength, with the basin of attraction providing insight into the probability of observed dynamical states.
Article
Mathematics
Yu-Ye Feng, Qing-Biao Wu
Summary: The article introduces a new iteration method MN-PGSOR for solving nonlinear systems with 2x2 block structure, combining PGSOR inner iteration and modified Newton method outer iteration, which shows superior performance in both local convergence and numerical results.
JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Tongxin Yan, Changfeng Ma
Summary: In this work, a modified generalized shift-splitting iteration method for complex symmetric linear systems is introduced, along with the convergence analysis and spectral properties of the corresponding preconditioned matrix. The effectiveness of the MGSS is demonstrated through a numerical example.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Automation & Control Systems
Eisa Khosravi Dehdezi, Saeed Karimi
Summary: In this paper, two attractive iterative methods - conjugate gradient squared (CGS) and conjugate residual squared (CRS) - are extended to solve the generalized coupled Sylvester tensor equations. The proposed methods use tensor computations with no maricizations involved. The numerical examples demonstrate the efficiency and performance advantages of the proposed methods compared to some existing algorithms.
TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL
(2021)
Article
Mathematics
Volodymyr Berezovski, Yevhen Cherevko, Irena Hinterleitner, Patrik Peska
Summary: In this paper, we investigate geodesic mappings from spaces with affine connections onto generalized 2-, 3-, and m-Ricci-symmetric spaces, and generalize the properties of these mappings.
Article
Mathematics, Applied
Ana L. Silvestre
Summary: The study focused on plane steady viscous liquid flow around a translating and rotating obstacle. The fundamental solution of the associated linearized problem was derived under the assumption of a general 2D rigid body velocity.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics, Applied
Sergey B. Kozitskiy, Mikhail Yu Trofimov, Pavel S. Petrov
Summary: In this study, a general approach to the numerical solution of iterative parabolic equations using the ETD pseudospectral method is developed. Pade-type iterative parabolic approximations are introduced to solve wave propagation problems more effectively.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Automation & Control Systems
Lingling Lv, Jinbo Chen, Zhe Zhang, Baowen Wang, Lei Zhang
Summary: This paper presents a finite iterative algorithm for solving periodic coupled matrix equations, and proves the convergence of the algorithm through theoretical derivation. The algorithm is applicable to any initial value and has a wide range of applications.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Yuyu He, Xiaofeng Wang, Weizhong Dai
Summary: Two coupled and decoupled dissipative finite difference schemes with high-order accuracy are proposed for solving the dissipative generalized symmetric regularized long wave equations in this paper. Dissipation of the discrete energy with different parameters is discussed, and the a priori estimate, existence and uniqueness of numerical solutions, convergence with O(tau 2+h4), and stability of the schemes are proved by the discrete energy method. Numerical examples are provided to support the theoretical analysis.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Automation & Control Systems
Xuesong Chen, Zebin Chen
Summary: This paper presents a modified conjugate gradient iterative (MCG) algorithm for solving generalized periodic multiple coupled Sylvester matrix equations, which can find the solution within finite iteration steps without round-off errors and provides a method for choosing initial matrices. Numerical examples illustrate the superior performance of the proposed method.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2021)
Article
Automation & Control Systems
Shahram Hosseini, M. Navabi, Masoud Hajarian
Summary: In this paper, a new online robust meta-heuristic adaptive LSQR (ORALSQR) estimation method is proposed for simultaneous estimation of a multi input/output linear dynamic model and system state variables. Numerical results show that this method outperforms the LS and RLS based estimation methods mentioned in this paper in terms of accuracy and robustness.
IET CONTROL THEORY AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Mostafa Abbaszadeh, Mahmoud A. Zaky, Ahmed S. Hendy, Mehdi Dehghan
Summary: In this paper, a numerical formulation with second-order accuracy in the time direction and spectral accuracy in the space variable is proposed for solving a nonlinear high-dimensional Rosenau-Burgers equation. The spectral element method and the two-grid idea are combined to simulate the equation, and a three-level algorithm is used for the proposed technique. The existence and uniqueness of the solutions to Steps 1, 2, and 3 are investigated, and error analysis is also discussed.
APPLIED NUMERICAL MATHEMATICS
(2023)
Article
Mathematics, Applied
Mostafa Abbaszadeh, Mohammad Ivan Azis, Mehdi Dehghan, Reza Mohammadi-Arani
Summary: This paper proposes a new meshless numerical procedure, namely the gradient smoothing method (GSM), for simulating the pollutant transition equation in urban street canyons. The time derivative is approximated using the finite difference scheme, while the space derivative is discretized using the gradient smoothing method. Additionally, the proper orthogonal decomposition (POD) approach is employed to reduce CPU time. Several real-world examples are solved to verify the efficiency of the developed numerical procedure.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Biology
Niusha Narimani, Mehdi Dehghan
Summary: This paper numerically studies the therapies of prostate cancer in a two-dimensional space. The proposed model describes the tumor growth driven by a nutrient and the effects of cytotoxic chemotherapy and antiangiogenic therapy. The results obtained without using any adaptive algorithm show the response of the prostate tumor growth to different therapies.
COMPUTERS IN BIOLOGY AND MEDICINE
(2023)
Article
Engineering, Multidisciplinary
Mostafa Abbaszadeh, Yasmin Kalhor, Mehdi Dehghan, Marco Donatelli
Summary: The purpose of this research is to develop a numerical method for option pricing in jump-diffusion models. The proposed model consists of a backward partial integro-differential equation with diffusion and advection factors. Pseudo-spectral technique and cubic B-spline functions are used to solve the equation, and a second-order Strong Stability Preserved Runge-Kutta procedure is adopted. The efficiency and accuracy of the proposed method are demonstrated through various test cases.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Engineering, Multidisciplinary
Mahboubeh Najafi, Mehdi Dehghan
Summary: In this work, two-dimensional dendritic solidification is simulated using the meshless Diffuse Approximate Method (DAM). The Stefan problem is studied through the phase-field model, considering both isotropic and anisotropic materials for comparisons. The effects of changing some constants on the obtained patterns are investigated.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Mathematics, Applied
Rooholah Abedian, Mehdi Dehghan
Summary: This paper presents a new formulation of conservative finite difference radial basis function weighted essentially non-oscillatory (WENO-RBF) schemes to solve conservation laws. Unlike previous methods, the flux function is generated directly with the conservative variables, and arbitrary monotone fluxes can be employed. Numerical simulations of several benchmark problems are conducted to demonstrate the good performance of the new scheme.
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
(2023)
Article
Mathematics, Applied
Majid Haghi, Mohammad Ilati, Mehdi Dehghan
Summary: In this paper, the cubic-quintic complex Ginzburg-Landau (CQCGL) equation is numerically studied in 1D, 2D, and 3D spaces. The equation is decomposed into three subproblems using the Strang splitting technique. Nonlinear ODEs are solved by the Runge-Kutta technique for the first and third problems, while a fourth-order RBF-generated Hermite finite difference (RBF-HFD) method is used for the second problem involving spatial derivatives. A temporal Richardson extrapolation technique is applied to improve the order of convergence in the time direction. Numerical results show that the proposed method improves the order of convergence and is accurate and efficient.
COMPUTATIONAL & APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Alireza Hosseinian, Pouria Assari, Mehdi Dehghan
Summary: This paper presents a numerical method for solving nonlinear Volterra integral equations with delay arguments. The method uses the discrete collocation approach with thin plate splines as a type of radial basis functions. The method provides an effective and stable algorithm to estimate the solution, which can be easily implemented on a personal computer. The error analysis and convergence validation of the method are also provided.
COMPUTATIONAL & APPLIED MATHEMATICS
(2023)
Article
Engineering, Multidisciplinary
Fatemeh Asadi-Mehregan, Pouria Assari, Mehdi Dehghan
Summary: This paper presents a computational algorithm for solving nonlinear systems of ordinary and partial differential equations resulting from HIV infection models. The method uses local radial basis functions as shape functions in the discrete collocation scheme, approximating the solution by a small set of nodes. The computational efficiency of the scheme is studied through several test examples.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Engineering, Multidisciplinary
Ali Ebrahimijahan, Mehdi Dehghan, Mostafa Abbaszadeh
Summary: In this study, the integrated radial basis functions-partition of unity (IRBF-PU) method is proposed for solving the coupled Schrodinger-Boussinesq equations in one-and two-dimensions. The IRBF-PU method is a local mesh-free method that offers flexibility and high accuracy for PDEs with smooth initial conditions. Numerical simulations demonstrate that the IRBF-PU method can effectively simulate solitary waves and preserve conservation laws. Furthermore, the obtained results are compared with other methods in the literature to validate the effectiveness and reliability of the proposed method.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Engineering, Multidisciplinary
Hasan Zamani-Gharaghoshi, Mehdi Dehghan, Mostafa Abbaszadeh
Summary: This article presents a numerical method for solving the surface Allen-Cahn model. The method is based on the generalized moving least-squares approximation and the closest point method. It does not depend on the structure of the underlying surface and only requires a set of arbitrarily distributed mesh-free points on the surface.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Computer Science, Interdisciplinary Applications
Raziyeh Erfanifar, Masoud Hajarian
Summary: This paper studies a common nonlinear matrix equation and proposes two iterative schemes to solve it, while proving the convergence of these schemes.
ENGINEERING COMPUTATIONS
(2023)
Article
Automation & Control Systems
Raziyeh Erfanifar, Masoud Hajarian
Summary: This study presents schemes based on the Hermitian and skew-Hermitian splitting to solve the quadratic matrix equation (QME), which is important in various fields. The results show that the proposed schemes converge to the solutions of the QME, and their applicability is verified through examples.
IET CONTROL THEORY AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Raziyeh Erfanifar, Masoud Hajarian, Khosro Sayevand
Summary: In this work, a family of fourth-order methods is proposed to solve nonlinear equations, which satisfy the Kung-Traub optimality conjecture. The efficiency indices of the methods are increased by developing them into memory methods. The methods are then extended to multi-step methods for solving systems of problems. Numerical examples are provided to confirm the theoretical results, and the methods are applied to solve nonlinear problems related to the numerical approximation of fractional differential equations.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
