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In this paper, based on the bifurcation theory, we numerically calculate and visualize non-trivial multiple solutions of the singularly perturbed Neumann problem on a square using the Jacobi pseudospectral method. Starting from the non-zero solution of the corresponding problem, we numerically obtain multiple positive solutions with various symmetries by the branch switching method. The bifurcation diagrams are drawn, displaying the symmetry breaking bifurcation phenomena of the singularly perturbed Neumann problem. Numerical results demonstrate the effectiveness of this method.

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Jacobi Pseudospectral Method for Computing the Multiple Solutions of a Singularly Perturbed Neumann Problem

  • 会议论文

  • 发表日期：

    2025年

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  • Peipei Wang,
  • Zhaoxiang Li,
  • Lixiang Jin,
  • Chunhua Shen

摘要

In this paper, based on the bifurcation theory, we numerically calculate and visualize non-trivial multiple solutions of the singularly perturbed Neumann problem on a square using the Jacobi pseudospectral method. Starting from the non-zero solution of the corresponding problem, we numerically obtain multiple positive solutions with various symmetries by the branch switching method. The bifurcation diagrams are drawn, displaying the symmetry breaking bifurcation phenomena of the singularly perturbed Neumann problem. Numerical results demonstrate the effectiveness of this method.