Symmetry and Automated Branch Following for a Semilinear Elliptic PDE on a Fractal Region

  title={Symmetry and Automated Branch Following for a Semilinear Elliptic PDE on a Fractal Region},
  author={John M. Neuberger and N{\'a}ndor Sieben and James W. Swift},
  journal={SIAM J. Applied Dynamical Systems},
We apply the Gradient-Newton-Galerkin-Algorithm (GNGA) of Neuberger & Swift to find solutions to a semilinear elliptic Dirichlet problem on the region whose boundary is the Koch snowflake. In a recent paper, we described an accurate and efficient method for generating a basis of eigenfunctions of the Laplacian on this region. In that work, we used the symmetry of the snowflake region to analyze and post-process the basis, rendering it suitable for input to the GNGA. The GNGA uses Newton’s… CONTINUE READING


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