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  • A Nearly Analytic Discrete Method for One-dimensional Unsteady Convection-dominated Diffusion Equations

    KIM YON-CHOL;YUN NAM;CHAI DONG-HO;

    In this paper, a nearly analytic discretization method for one-dimensional linear unsteady convection-dominated diffusion equations and viscous Burgers' equation as one of the nonlinear equation is considered. In the case of linear equations,we find the local truncation error of the scheme is O(τ~2+ h~4) and consider the stability analysis of the method on the basis of the classical von Neumann's theory. In addition, the nearly analytic discretization method for the one-dimensional viscous Burgers' equation is also constructed. The numerical experiments are performed for several benchmark problems presented in some literatures to illustrate the theoretical results. Theoretical and numerical results show that our method is to be higher accurate and nonoscillatory and might be helpful particularly in computations for the unsteady convection-dominated diffusion problems.

    2019年03期 v.35 193-207页 [查看摘要][在线阅读][下载 588K]
  • Multiple Positive Solutions to Singular Fractional Differential System with Riemann-Stieltjes Integral Boundary Condition

    ZHANG HAI-YAN;LI YAO-HONG;

    In this paper, we study a class of singular fractional differential system with Riemann-Stieltjes integral boundary condition by constructing a new cone and using Leggett-Williams fixed point theorem. The existence of multiple positive solutions is obtained. An example is presented to illustrate our main results.

    2019年03期 v.35 208-218页 [查看摘要][在线阅读][下载 167K]
  • Planar Cubic G~1 Hermite Interpolant with Minimal Quadratic Oscillation in Average

    LI JUN-CHENG;

    In this paper we apply a new method to choose suitable free parameters of the planar cubic G1 Hermite interpolant. The method provides the cubic G1 Hermite interpolant with minimal quadratic oscillation in average. We can use the method to construct the optimal shape-preserving interpolant. Some numerical examples are presented to illustrate the effectiveness of the method.

    2019年03期 v.35 219-224页 [查看摘要][在线阅读][下载 228K]
  • Common Fixed Points for Two Mappings with Implicit-linear Contractions on Partially Ordered 2-metric Spaces

    PIAO YONG-JIE;

    In this paper, we introduce a new class U of 3-dimensional real functions, use U and a 2-dimensional real function ? to construct a new implicit-linear contractive condition and obtain some existence theorems of common fixed points for two mappings on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point. The obtained results goodly generalize and improve the corresponding conclusions in references.

    2019年03期 v.35 225-234页 [查看摘要][在线阅读][下载 157K]
  • Fekete-Szeg? Inequality for a Subclass of Bi-univalent Functions Associated with Hohlov Operator and Quasi-subordination

    GUO DONG;TANG HUO;AO EN;XIONG LIANG-PENG;

    In this paper, we introduce a new subclass of bi-univalent functions defined by quasi-subordination and Hohlov operator and obtain the coefficient estimates and Fekete-Szeg? inequality for function in this new subclass. The results presented in this paper improve or generalize the recent works of other authors.

    2019年03期 v.35 235-246页 [查看摘要][在线阅读][下载 171K]
  • An SIRS Epidemic Model with Pulse Vaccination, Birth Pulse and Logistic Death Rate

    GAO JIAN-ZHONG;ZHANG TAI-LEI;

    In this paper, we propose an SIRS epidemic model with pulse vaccination, birth pulse and Logistic death rate. By using the stroboscopic map of a discrete dynamical system, the disease-free periodic solution(DFPS for short) of the model under pulse vaccination and birth pulse is obtained. Based on the Floquet theory and comparison theorem of impulsive differential equations, the global asymptotic stability of the DFPS is given, and sufficient conditions for the permanence of the model are obtained. In addition, numerical simulations are done to confirm our theoretical results.

    2019年03期 v.35 247-263页 [查看摘要][在线阅读][下载 1104K]
  • An Optimal Sixth-order Finite Difference Scheme for the Helmholtz Equation in One-dimension

    LIU XU;WANG HAI-NA;HU JING;

    In this paper,we present an optimal 3-point finite difference scheme for solving the 1D Helmholtz equation.We provide a convergence analysis to show that the scheme is sixth-order in accuracy.Based on minimizing the numerical dispersion,we propose a refined optimization rule for choosing the scheme’s weight parameters.Numerical results are presented to demonstrate the efficiency and accuracy of the optimal finite difference scheme.

    2019年03期 v.35 264-272页 [查看摘要][在线阅读][下载 162K]
  • The Transfer Ideal under the Action of a Nonmetacyclic Group in the Modular Case

    JIA PAN-PAN;NAN JI-ZHU;

    Let Fq be a finite field of characteristic p(p≠= 2) and V_4 a four-dimensional F_q-vector space. In this paper, we mainly determine the structure of the transfer ideal for the ring of polynomials F_q[V_4] under the action of a nonmetacyclic p-group P in the modular case. We prove that the height of the transfer ideal is 1 using the fixed point sets of the elements of order p in P and that the transfer ideal is a principal ideal.

    2019年03期 v.35 273-282页 [查看摘要][在线阅读][下载 170K]
  • Further Results on Meromorphic Functions and Their nth Order Exact Differences with Three Shared Values

    CHEN SHENG-JIANG;XU AI-ZHU;LIN XIU-QIANG;

    Let E(a, f) be the set of a-points of a meromorphic function f(z) counting multiplicities. We prove that if a transcendental meromorphic function f(z) of hyper order strictly less than 1 and its nth exact difference ?_c~nf(z) satisfy E(1, f) =E(1, ?_c~nf), E(0, f) ? E(0, ?_c~nf) and E(∞, f) ? E(∞, ?_c~nf), then ?_c~nf(z) ≡ f(z).This result improves a more recent theorem due to Gao et al.(Gao Z, Kornonen R,Zhang J, Zhang Y. Uniqueness of meromorphic functions sharing values with their nth order exact differences. Analysis Math., 2018, https://doi.org/10.1007/s10476-018-0605-2) by using a simple method.

    2019年03期 v.35 283-288页 [查看摘要][在线阅读][下载 144K]
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