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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 value for n - persons games 显示文摘 | SHAPLEY L S | 1953 | Annals of Mathematics Studies1953，，28： | 1 |
| 9 | The method of path coefficient显示文摘 | Wright S | 1934 | Annals of Mathematical Studies1934，，5： | 1 |
| 10 | A bargaining model for the cooperative n-person game 显示文摘 | Harsanyi J | 1959 | Annals of Mathematics Study1959，40，： | 1 |
| 11 | Nonstandard Analysis by Axiomatic Method显示文摘 | Tom Kawai | 1983 | Studies in Logic and the Foundations of Mathematics Volume 1111983，，： | 1 |
| 12 | Infinite Forcing in Model Theory 显示文摘 | Abraham Robinson | 1971 | Studies in Logic and the Foundations of Mathematics Volume 631971，，： | 1 |
| 13 | A Value for n-Person Games显示文摘 | ShapleyL S | 1953 | Annales of Mathematics Studies1953，28，3： | 1 |
| 14 | A value for n-persons games显示文摘 | Shapley L S | 1953 | Annals of Mathematics Studies1953，，28： | 1 |
| 15 | A value for n-persons games显示文摘 | Shapley L | 1953 | Annals of Mathematics Studies1953，28，7： | 1 |
| 16 | A value for n2persons games显示文摘 | Shapley L S | 1953 | Annals of Mathematics Studies1953，，28： | 1 |
| 17 | A value for n-person games显示文摘 | Shapley L S | 1953 | Annals of Mathematics Studies1953，28，： | 1 |
| 18 | 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 |
| 19 | A min-max solution of an inventory problem 显示文摘 | Scarf H | 1957 | Studies in the Mathematical Theory of Inventory and Production1957，25，2： | 1 |
| 20 | A value for n-person games显示文摘 | Shapley L S | 1953 | Contributions to the Theory of Games Annals of Mathematics Studies Princeton University Press Princeton N J1953，28，2： | 1 |
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