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椭圆型界面问题的破裂再生核方法

杨学敏, 牛晶, 姚春华   

  1. 哈尔滨师范大学 数学科学学院, 哈尔滨 150025
  • 收稿日期:2021-03-24 出版日期:2022-05-14 发布日期:2022-05-06
  • 通讯作者: 牛晶,Email:qq63192678@126.com.
  • 基金资助:
    哈尔滨师范大学硕士研究生创新科研项目(HSDSSCX2021-13)和国家青年自然科学基金项目 (12101164) 资助.

杨学敏, 牛晶, 姚春华. 椭圆型界面问题的破裂再生核方法[J]. 计算数学, 2022, 44(2): 217-232.

Yang Xuemin, Niu Jing, Yao Chunhua. BROKEN REPRODUCING KERNEL METHOD FOR ELLIPTIC TYPE INTERFACE PROBLEMS[J]. Mathematica Numerica Sinica, 2022, 44(2): 217-232.

BROKEN REPRODUCING KERNEL METHOD FOR ELLIPTIC TYPE INTERFACE PROBLEMS

Yang Xuemin, Niu Jing, Yao Chunhua   

  1. School of Mathematics and Sciences, Harbin Normal University, Harbin 150025, China
  • Received:2021-03-24 Online:2022-05-14 Published:2022-05-06
本文基于一维椭圆型界面问题提出了一种有效的数值方法.首先,根据模型构建一个崭新的破裂再生核空间.其次,应用破裂再生核方法给出了此类界面问题的近似解,并讨论该方法的收敛性.最后,通过几个有效的数值算例来说明该方法的精确性和稳定性.
In this paper, based on the problem of one-dimensional elliptic interface, an effective numerical method is proposed. First of all, a brand-new broken reproducing kernel space is built according to the model. Secondly, the approximate solution of this kind of interface problems is given by using the broken reproducing kernel method, and then we discuss the convergence of the method. Finally, the accuracy and stability of this method are explained by several valid numerical examples.

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