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数学研究及应用
数学研究及应用

王仁宏

双月刊

2095-2651

jmre@dlut.edu.cn

0411-84707392

116024

大连理工大学应用数学系

数学研究及应用/Journal Journal of mathematical research with applicationsCSCD北大核心CSTPCD
查看更多>>本刊是国家教育部主管、大连理工大学主办的数学类学术性刊物。其宗旨是推进数学研究、评论数学研究、及时报道数学理论成果与应用数学成果。主要刊载有关数学的原创性的高质量的论文、研究简报、研究通讯；国内外数学著作的评论；数学方法论、数理哲学方面的文章。还介绍某些新兴边缘学科的数学研究方法及数学新分支，反映国内外数学工作者提出的未解决问题及国内外重要数学学术研究动态。读者对象是数学工作者、大专院校数学教师、理工科研究生、数学和力学专业高年级学生、有关科技工作者以及其他数学爱好者。
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    Unconditional and Optimal Pointwise Error Estimates of Finite Difference Methods for the Two-Dimensional Complex Ginzburg-Landau Equation

    Yue CHENGDongsheng TANG
    248-268页
    查看更多>>摘要：In this paper,we give improved error estimates for linearized and nonlinear Crank-Nicolson type finite difference schemes of Ginzburg-Landau equation in two dimensions.For linearized Crank-Nicolson scheme,we use mathematical induction to get unconditional error estimates in discrete L2 and H1 norm.However,it is not applicable for the nonlinear scheme.Thus,based on a'cut-off'function and energy analysis method,we get unconditional L2 and H1 error estimates for the nonlinear scheme,as well as boundedness of numerical solutions.In addition,if the assumption for exact solutions is improved compared to before,unconditional and optimal pointwise error estimates can be obtained by energy analysis method and several Sobolev inequalities.Finally,some numerical examples are given to verify our theoretical analysis.
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    Linear and Nonlinear Solutions of Interfacial Waves Due to a Doublet

    Di LIUZhen WANG
    269-284页
    查看更多>>摘要：Steady two-dimensional potential flows of two-layer fluids with a submerged doublet in the lower layer are considered.Both linear analytical solutions and fully nonlinear solutions based on boundary integral equation methods are obtained.Nonlinearity strongly influences the downstream wave height and leads to a slight phase difference.When the Froude number is small,wave height fast gets its maximum as the Froude number increases.While wave-less solutions may be obtained if the Froude number is very large.Afterward,the interfacial waves due to one point vortex or a vortex pair are compared with those due to a doublet.It is found that the nonlinear wave profiles due to a doublet are quite close to those due to a vertical vortex pair if the distance between the vortex pair is set appropriately.
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