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| 1 | Generalized Jacobi Spectral-Galerkin Method for Nonlinear Volterra Integral Equations with Weakly Singular Kernels显示文摘We propose a generalized Jacobi spectral-Galerkin method for the nonlinear Volterra integral equations(VIEs)with weakly singular kernels.We establish the existence and uniqueness of the numerical solution,and characterize the convergence of the proposed method under reasonable assumptions on the nonlinearity.We also present numerical results which are consistent with the theoretical predictions. | Jie Shen Changtao Sheng Zhongqing Wang | 2015 | Journal of Mathematical Study2015，48，4： | 4 |
| 2 | Convergence Analysis of anUnconditionally Energy Stable Linear Crank-Nicolson Scheme for the Cahn-Hilliard Equation显示文摘Efficient and unconditionally stable high order time marching schemes are very important but not easy to construct for nonlinear phase dynamics.In this paper,we propose and analysis an efficient stabilized linear Crank-Nicolson scheme for the Cahn-Hilliard equation with provable unconditional stability.In this scheme the nonlinear bulk force are treated explicitly with two second-order linear stabilization terms.The semi-discretized equation is a linear elliptic systemwith constant coefficients,thus robust and efficient solution procedures are guaranteed.Rigorous error analysis show that,when the time step-size is small enough,the scheme is second order accurate in time with a prefactor controlled by some lower degree polynomial of 1/#.Here#is the interface thickness parameter.Numerical results are presented to verify the accuracy and efficiency of the scheme. | Lin Wang Haijun Yu | 2018 | Journal of Mathematical Study2018，51，1： | 2 |
| 3 | New Alternately Linearized Implicit Iteration for M-matrix Algebraic Riccati Equations显示文摘Research on the theories and the efficient numerical methods of M-matrix algebraic Riccati equation(MARE)has become a hot topic in recent years due to its broad applications.In this paper,based on the alternately linearized implicit iteration method(ALI)[Z.-Z.Bai et al.,Numer.Linear Algebra Appl.,13(2006),655-674.],we propose a new alternately linearized implicit iteration method(NALI)for computing the minimal nonnegative solution of M-matrix algebraic Riccati equation.Convergence of the NALI method is proved by choosing proper parameters for the MARE associated with nonsingular M-matrix or irreducible singular M-matrix.Theoretical analysis and numerical experiments show that the NALI method is more efficient than the ALI method in some cases. | Jinrui Guan Linzhang Lu | 2017 | Journal of Mathematical Study2017，50，1： | 2 |
| 4 | One-Side Derived Categories of Pre-Strict P-Semi-Abelian Categories显示文摘In this paper,we study a class of P-semi-abelian categories,as well as left and right cohomological functors.Then we establish the corresponding one-side derived categories. | Liangyu Chen Lin Xin | 2015 | Journal of Mathematical Study2015，48，4： | 2 |
| 5 | Spectral Method for the Black-Scholes Model of American Options Valuation显示文摘In this paper,we devote ourselves to the research of numerical methods for American option pricing problems under the Black-Scholes model.The optimal exercise boundary which satisfies a nonlinear Volterra integral equation is resolved by a high-order collocationmethod based on gradedmeshes.For the other spatial domain boundary,an artificial boundary condition is applied to the pricing problem for the effective truncation of the semi-infinite domain.Then,the front-fixing and stretching transformations are employed to change the truncated problemin an irregular domain into a one-dimensional parabolic problem in[−1,1].The Chebyshev spectral method coupledwith fourth-order Runge-Kuttamethod is proposed for the resulting parabolic problem related to the options.The stability of the semi-discrete numerical method is established for the parabolic problemtransformed fromthe originalmodel.Numerical experiments are conducted to verify the performance of the proposed methods and compare them with some existing methods. | Haiming Song Ran Zhang WenYi Tian | 2014 | Journal of Mathematical Study2014，47，1： | 2 |
| 6 | On L^(2)-Stability Analysis of Time-Domain Acoustic Scattering Problems with Exact Nonreflecting Boundary Conditions显示文摘This paper is devoted to stability analysis of the acoustic wave equation exterior to a bounded scatterer,where the unbounded computational domain is truncated by the exact time-domain circular/spherical nonreflecting boundary condition(NRBC).Different from the usual energy method,we adopt an argument that leads to L^(2)-a priori estimates with minimum regularity requirement for the initial data and source term.This needs some delicate analysis of the involved NRBC.These results play an essential role in the error analysis of the interior solvers(e.g.,finite-element/spectral-element/spectral methods)for the reduced scattering problems.We also apply the technique to analyze a time-domain waveguide problem. | Bo Wang Li-Lian Wang | 2014 | Journal of Mathematical Study2014，47，1： | 2 |
| 7 | Existence of solution for a three-point boundary value problem of nonlinear fractional differential equation显示文摘 | HAN Ren-ji JIANG Wei | 2011 | Journal of Mathematical Study2011，44，2： | 1 |
| 8 | A Comparative Numerical Study of Meshing Functionals for Variational Mesh Adaptation显示文摘We present a comparative numerical study for three functionals used for variational mesh adaptation.One of them is a generalization ofWinslow’s variable diffusion functional while the others are based on equidistribution and alignment.These functionals are known to have nice theoretical properties and work well for most mesh adaptation problems either as a stand-alone variational method or combined within the moving mesh framework.Their performance is investigated numerically in terms of equidistribution and alignment mesh quality measures.Numerical results in 2D and 3D are presented. | Weizhang Huang Lennard Kamenski Robert D.Russell | 2015 | Journal of Mathematical Study2015，48，2： | 1 |
| 9 | A Domain Decomposition Chebyshev Spectral Collocation Method for Volterra Integral Equations显示文摘We develop a domain decomposition Chebyshev spectral collocationmethod for the second-kind linear and nonlinear Volterra integral equations with smooth kernel functions.The method is easy to implement and possesses high accuracy.In the convergence analysis,we derive the spectral convergence order under the L¥-norm without the Chebyshev weight function,and we also show numerical examples which coincide with the theoretical analysis. | Hua Wu Yunzhen Zhu Hailu Wang Lingfang Xu | 2018 | Journal of Mathematical Study2018，51，1： | 1 |
| 10 | Conditional Residual Lifetimes of(n−k+1)-out-of-n Systems with Mixed Erlang Components显示文摘We consider an(n−k+1)-out-of-n system with component lifetimes being correlated.The main objective of this paper is to study the conditional residual lifetime of an(n−k+1)-out-of-n system,given that at a fixed time a certain number of components have failed,assuming that the component lifetimes follow a multivariate Erlang mixture.Comparison studies of the stochastic ordering of the(n−k+1)-out-ofn system are presented.Several examples are presented to illustrate and confirm our results. | Wenyong Gui Rongtan Huang Jianhua Lin X.Sheldon Lin | 2017 | Journal of Mathematical Study2017，50，1： | 1 |
| 11 | Efficient Spectral Methods for Transmission Eigenvalues and Estimation of the Index of Refraction显示文摘An important step in estimating the index of refraction of electromagnetic scattering problems is to compute the associated transmission eigenvalue problem.We develop in this paper efficient and accurate spectral methods for computing the transmission eigenvalues associated to the electromagnetic scattering problems.We present ample numerical results to show that our methods are very effective for computing transmission eigenvalues(particularly for computing the smallest eigenvalue),and together with the linear samplingmethod,provide an efficient way to estimate the index of refraction of a non-absorbing inhomogeneous medium. | Jing An Jie Shen | 2014 | Journal of Mathematical Study2014，47，1： | 1 |
| 12 | On Unitary Invariant Strongly Pseudoconvex Complex Landsberg Metrics显示文摘In this paper,we prove that a unitary invariant strongly pseudoconvex complex Finsler metric is a complex Landsberg metric if and if only if it comes from a unitary invariant Hermitian metric.This implies that there does not exist unitary invariant complex Landsberg metric unless it comes from a unitary invariant Hermitian metric. | Yong He Chun-Ping Zhong | 2016 | Journal of Mathematical Study2016，49，1： | 1 |
| 13 | Some Inequalities Related to the Degree Sequence of a Graph显示文摘 | Xiao-nong Huang | 2009 | Journal of Mathematical Study2009，，35： | 1 |
| 14 | Relationship between girth and acyclic edge chromatic number of graphs 显示文摘 | SUN Yi-rong YAN Jing-zhi | 2005 | Journal of Mathematical Study (Series B)2005，95，： | 1 |
| 15 | Oscillation for a class of nonlinear fractional differential equations with damping term显示文摘 | Zheng B | 2013 | Journal of Advanced Mathematical Studies2013，6，1： | 1 |
| 16 | Oscillation for a class of nonlinear fractional differential equations with damping term显示文摘 | Zheng B | 2013 | Journal of Advanced Mathematical Studies2013，6，1： | 1 |
| 17 | Boundedness Characterization of Maximal Commutators on Orlicz Spaces in the Dunkl Setting显示文摘On the real line,the Dunkl operators Dν(f)(x):=d f(x)dx+(2ν+1)f(x)−f(−x)2x,∀x∈R,∀ν≥−12 are differential-difference operators associated with the reflection group Z2 on R,and on the Rd the Dunkl operators{Dk,j}dj=1 are the differential-difference operators associated with the reflection group Zd2 on Rd.In this paper,in the setting R we show that b∈BMO(R,dmν)if and only if the maximal commutator Mb,νis bounded on Orlicz spaces LΦ(R,dmν).Also in the setting Rd we show that b∈BMO(Rd,h2k(x)dx)if and only if the maximal commutator Mb,k is bounded on Orlicz spaces LΦ(Rd,h2k(x)dx). | Vagif S.Guliyev Yagub Y.Mammadov Fatma A.Muslumova | 2020 | Journal of Mathematical Study2020，53，1： | 1 |
| 18 | Compatibility Evaluation of Consolidation Treatments in Monuments Scale 显示文摘 | Moropoulou A Theoulakis P Tsiourva Th | 2000 | Journal of European Study Group on Physical Chemical and Bi- ologiccal and Mathematical Techniques Applied to Archaeology2000，59，： | 1 |
| 19 | An Equivalent Characterization of CMO(R^(n)) with Ap Weights显示文摘Let 1 | Minghui Zhong Xianming Hou | 2020 | Journal of Mathematical Study2020，53，1： | 0 |
| 20 | Numerical Approaches to Compute Spectra of Non-Self Adjoint Operators and Quadratic Pencils显示文摘In this article we are interested in the numerical computation of spectra of non-self adjoint quadratic operators.This leads to solve nonlinear eigenvalue problems.We begin with a review of theoretical results for the spectra of quadratic operators,especially for the Schr¨odinger pencils.Then we present the numerical methods developed to compute the spectra:spectral methods and finite difference discretization,in infinite or in bounded domains.The numerical results obtained are analyzed and compared with the theoretical results.The main difficulty here is that we have to compute eigenvalues of strongly non-self-adjoint operators which are very unstable. | Fatima Aboud Francois Jauberteau Guy Moebs Didier Robert | 2020 | Journal of Mathematical Study2020，53，1： | 0 |
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