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

@article{Neuberger2006SymmetryAA,
  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},
  year={2006},
  volume={5},
  pages={476-507}
}
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

References

Publications referenced by this paper.
Showing 1-10 of 28 references

The Symmetry Perspective: from Equilibrium to Chaos in Phase Space and Physical Space, Progress

  • M. Golubitsky, I. Stewart
  • 2002
Highly Influential
10 Excerpts

Singularities and Groups in Bifurcation Theory, Volume 2

  • M. Golubitsky, I. Stewart, D. G. Schaefer
  • Applied Mathematical Sciences
  • 1988
Highly Influential
10 Excerpts

Group Theory and Quantum Mechanics, McGraw-Hill Book Co., New York-Toronto

  • M. Tinkham
  • Ont.-London,
  • 1964
Highly Influential
4 Excerpts

Sign-Changing Solutions for a Superlinear Dirichlet Problem, Rocky Mnt

  • A. Castro, J. Cossio, J. M. Neuberger
  • J. Math 27,
  • 1997
Highly Influential
4 Excerpts

Snowflake Harmonics and Computer Graphics: Numerical Computation of Spectra on Fractal Drums

  • M. L. Lapidus, J. W. Neuberger, R. L. Renka, C. A. Griffith
  • International Journal Bifurcation and Chaos 6,
  • 1996
Highly Influential
4 Excerpts

An Efficient and Stable Method for Computing Saddle Points with Symmetries

  • J. Zhou, Z.-Q. Wang
  • SIAM J. Num. Anal.,
  • 2005
1 Excerpt

Estimating Solutions for the Ginzburg-Landau Superconductivity Model in Thin Disks

  • T. J. Thompson
  • Northern Arizona University,
  • 2005
2 Excerpts

Newton’s Method for Solutions of a Ginzburg-Landau Equation on a Thin Disk

  • J. M. Neuberger, J. W. Swift, T. J. Thompson
  • in preparation,
  • 2005
1 Excerpt

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