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运用Poincaré-Miranda定理数值验证变分不等式解的存在性

江正华1, 牛欣2, 朱楚1   

  1. 1. 南京大学数学系, 南京 210093;
    2. 合肥学院 数学与物理系, 合肥 230601
  • 收稿日期:2019-04-02 发布日期:2021-02-04
  • 基金资助:
    江苏省优势学科(南京大学数学学科)项目(No.14403301)和江苏省高等教育实验教学示范中心建设专项经费(No.001520)资助.

江正华, 牛欣, 朱楚. 运用Poincaré-Miranda定理数值验证变分不等式解的存在性[J]. 计算数学, 2021, 43(1): 56-69.

Jiang Zhenghua, Niu Xin, Zhu Chu. NUMERICAL VALIDATION OF THE EXISTENCE OF SOLUTIONS FOR VARIATIONAL INEQUALITY PROBLEM VIA POINCARé-MIRANDA THEOREM[J]. Mathematica Numerica Sinica, 2021, 43(1): 56-69.

NUMERICAL VALIDATION OF THE EXISTENCE OF SOLUTIONS FOR VARIATIONAL INEQUALITY PROBLEM VIA POINCARé-MIRANDA THEOREM

Jiang Zhenghua1, Niu Xin2, Zhu Chu1   

  1. 1. Department of Mathematics, Nanjing University, Nanjing 210093, China;
    2. Department of Mathematics, Hefei University, Hefei 230601, China
  • Received:2019-04-02 Published:2021-02-04
本文运用Poincaré-Miranda定理数值验证变分不等式问题解的存在性. 证明这一新方法相对于已有的方法更具有普遍性, 并通过数值例子说明本方法的高效性.
In this paper, by using the Poincaré-Miranda theorem, we establish a numerical method to validate the existence of solutions for variational inequality problem. It is proved that this new method is more universal than the existing methods. Numerical experiments show the efficiency of the method.

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