Article
Mathematics, Applied
Jinkui Liu, Ning Zhang, Jing Wang, Zuliang Lu
Summary: An approximate gradient-type method is proposed in this paper to solve nonlinear symmetric equations with convex constraints based on the projection operator and pseudo-monotone property. This method does not require precise gradient or Jacobian matrix information, but only uses approximate substitutions based on the symmetric property of equations. Under appropriate assumptions, global convergence and R-linear convergence rate are proven. Numerical experiments demonstrate the stability and effectiveness of the proposed method for test problems.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Hongwei Zhang, Xiao Su
Summary: In this paper, a class of wave equations of Hartree type on a bounded smooth convex domain with Dirichlet boundary condition is considered. The local existence result is obtained by applying the standard semigroup theory. The condition of global existence of weak solutions is derived using potential well theory. Blowup results for solutions when the initial energy is nonnegative or negative are given with the help of potential well theory and convexity method.
STUDIES IN APPLIED MATHEMATICS
(2022)
Article
Chemistry, Physical
F. Arias de Saavedra, E. Buendia, F. J. Galvez
Summary: The study focuses on the ground state of the confined beryllium atom under penetrable spherical walls of Gaussian type, analyzing the total energy and its partial contributions, as well as the behavior of single particle energies and density. The Numerical Parameterized Optimized Effective Potential method is used for all calculations.
CHEMICAL PHYSICS LETTERS
(2021)
Article
Mathematics, Applied
Francesco Casella, Bernhard Bachmann
Summary: This paper introduces criteria for analyzing the influence of initial guesses on the evolution of Newton-Raphson's algorithm, and identifies which initial guesses need to be improved in case of convergence failure. By introducing indicators based on first and second derivatives of the residual function, the impact of each variable's initial guess on convergence failure can be assessed.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Operations Research & Management Science
Kabiru Ahmed, Mohammed Yusuf Waziri, Salisu Murtala, Abubakar Sani Halilu, Jamilu Sabi'u
Summary: In this paper, a new DL-type projection algorithm is proposed for large-dimension nonlinear monotone problems with signal reconstruction and image recovery applications. The algorithm achieves global convergence by incorporating another optimal choice of the DL parameter based on the eigenvalue study of a symmetric DL-type iteration matrix into a five-term direction scheme. Numerical experiments demonstrate the efficiency of the algorithm in solving nonlinear monotone problems as well as l(1) - norm regularized problems in compressed sensing by comparing it with recent DL-type methods.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Haitong Li, Jingyu Li, Ming Mei, Kaijun Zhang
Summary: This paper discusses the Cauchy problem for the one-dimensional compressible Euler equations with critical time-dependent overdamping, proving the existence of a unique global solution converging to the corresponding nonlinear diffusion wave in the critical case. The optimal convergence rate in logarithmic form is derived using the technical time-weighted method.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Muhammad Abdullahi, Auwal Bala Abubakar, Yuming Feng, Jinkui Liu
Summary: This paper proposes a derivative-free iterative technique for solving nonlinear monotone equations with convex constraints. Some issues in the work by Liu and Feng (Numer. Algoritm. 82(1):245-262, 2019) are pointed out and necessary adjustments and bounds are established. The global convergence of the proposed approach is proven, and numerical results are provided to support the adjustments.
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics, Applied
Jiani Wang, Xiao Wang, Liwei Zhang
Summary: In this paper, the authors study stochastic regularized Newton methods for finding zeros of nonlinear equations using approximations accessed through calls to stochastic oracles. The authors propose an algorithm that computes a regularized Newton step to handle potential singularity of Jacobian approximations. They investigate the global convergence properties and convergence rate of the proposed algorithm. Additionally, they propose a stochastic regularized Newton method incorporating a variance reduction technique and establish the corresponding sample complexities to find an approximate solution in terms of the total number of stochastic oracle calls.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Physics, Mathematical
Masahiro Suzuki, Katherine Zhiyuan Zhang
Summary: In this paper, we investigate the compressible Navier-Stokes equation in a perturbed half-space with an outflow boundary condition and the supersonic condition. We demonstrate the unique existence of stationary solutions for the perturbed half-space, which exhibit multidirectional flow and are independent of the tangential directions. Additionally, we prove the asymptotic stability of these stationary solutions.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2021)
Article
Mathematics, Applied
Miguel Angel Hernandez-Veron, Natalia Romero-Alvarez
Summary: In this paper, we study the simplest quadratic matrix equation and propose an iterative scheme based on the Krasnoselskij method, which is more accurate than the traditional successive approximation method. Numerical experiments also demonstrate the effectiveness of using the Krasnoselskij method as a predictor and the Newton method as a corrector in the iterative scheme.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Hassan Mohammad, Aliyu Muhammed Awwal
Summary: A derivative-free diagonal Polak-Ribiere-Polyak like algorithm is presented for solving large-scale systems of nonlinear equations. The algorithm obtains the search direction by incorporating a positive definite diagonal matrix with the positive Polak-Ribiere-Polyak (PRP+) parameter. The algorithm achieves global convergence and convergence rate by employing a derivative-free line search technique. Numerical experiments demonstrate the good performance of the algorithm on some large-scale systems of nonlinear equations.
NUMERICAL ALGORITHMS
(2022)
Article
Mathematics, Interdisciplinary Applications
Fouad Othman Mallawi, Ramandeep Behl, Prashanth Maroju
Summary: There are few papers on the global convergence of iterative methods using Banach spaces. This paper focuses on discussing the global convergence of a third-order iterative method. The convergence analysis is proposed under the assumption that the first-order Frechet derivative satisfies the continuity condition of the Holder. Furthermore, some integral equations and boundary value problems are considered to illustrate the practical applicability of the theoretical results.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Chuan-gang Kang, Heng Zhou
Summary: This paper investigates a new error term for Kaczmarz-type methods and establishes the corresponding convergence rates. By estimating the new error term for the Kaczmarz method, a simpler proof for its convergence can be obtained.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Zhongwei Shen
Summary: This article examines Darcy's law for an incompressible viscous fluid flowing in a porous medium. The paper establishes the O(root epsilon) convergence rate by constructing two boundary layer correctors to control the boundary layers created by the incompressibility condition and the discrepancy of boundary values.
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Interdisciplinary Applications
Yang Liu, Li Zhang
Summary: In this paper, the initial boundary value problem for a fractional viscoelastic equation of the Kirchhoff type is studied. A potential well is defined in suitable functional spaces. By using Galerkin approximations in the framework of the potential well theory, the global existence of solutions is obtained. Furthermore, the asymptotic behavior of solutions is derived by means of the perturbed energy method. The main results provide sufficient conditions for the qualitative properties of solutions in time.
FRACTAL AND FRACTIONAL
(2022)
Article
Physics, Mathematical
Li Chen, Ji Oon Lee, Jinyeop Lee
JOURNAL OF MATHEMATICAL PHYSICS
(2018)
Article
Multidisciplinary Sciences
Sangryun Lee, Jinyeop Lee, Byungki Ryu, Seunghwa Ryu
SCIENTIFIC REPORTS
(2018)
Article
Materials Science, Multidisciplinary
Sangryun Lee, Jinyeop Lee, Seunghwa Ryu
MATHEMATICS AND MECHANICS OF SOLIDS
(2019)
Article
Materials Science, Multidisciplinary
Sangryun Lee, Youngsoo Kim, Jinyeop Lee, Seunghwa Ryu
MATHEMATICS AND MECHANICS OF SOLIDS
(2019)
Review
Materials Science, Multidisciplinary
Seunghwa Ryu, Sangryun Lee, Jiyoung Jung, Jinyeop Lee, Youngsoo Kim
FRONTIERS IN MATERIALS
(2019)
Article
Physics, Mathematical
Jinyeop Lee
JOURNAL OF STATISTICAL PHYSICS
(2019)
Correction
Multidisciplinary Sciences
Sangryun Lee, Jinyeop Lee, Byungki Ryu, Seunghwa Ryu
SCIENTIFIC REPORTS
(2019)
Article
Physics, Mathematical
Li Chen, Jinyeop Lee, Matthew Liew
Summary: In this study, the time dependent Schrodinger equation for large spinless fermions with semiclassical scale =N-1/3 in three dimensions is examined. By utilizing the Husimi measure defined by coherent states, the Schrodinger equation is rewritten into a BBGKY type of hierarchy for the k particle Husimi measure. Further estimates are made to obtain weak compactness of the Husimi measure, and uniform estimates for the remainder terms in the hierarchy are derived to demonstrate that the weak limit of the Husimi measure in the semiclassical regime is exactly the solution of the Vlasov equation.
JOURNAL OF STATISTICAL PHYSICS
(2021)
Article
Physics, Multidisciplinary
Li Chen, Jinyeop Lee, Matthew Liew
Summary: This study focuses on the quantum dynamics of N interacting fermions in the large N limit, deriving the Vlasov-Poisson system from the quantum system by simultaneously estimating the semiclassical and mean-field residues in terms of the Husimi measure.
ANNALES HENRI POINCARE
(2022)
Article
Mathematics
Sung-Soo Byun, Nam-Gyu Kang, Ji Oon Lee, Jinyeop Lee
Summary: In this study, we investigate the real eigenvalues of a class of (N x N) real elliptic Ginibre matrix whose entries are correlated through a non-Hermiticity parameter tau(N) is an element of [0, 1]. In the almost-Hermitian regime, where 1 - tau(N) = Theta(N-1), we derive the large-N expansion of the mean, variance, and limiting density of the number of real eigenvalues.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
(2023)
Article
Mathematics, Applied
Jinyeop Lee, Alessandro Michelangeli
Summary: This study reviews the challenges in understanding fragmented condensates, refines previous characterizations in terms of marginals, and provides a quantitative convergence rate to the leading effective dynamics in the double limit of infinitely many particles and infinite energy gap.
