Efficient gluing of numerical continuation and a multiple solution method for elliptic PDEs

@article{Kuehn2015EfficientGO,
  title={Efficient gluing of numerical continuation and a multiple solution method for elliptic PDEs},
  author={C. Kuehn},
  journal={Appl. Math. Comput.},
  year={2015},
  volume={266},
  pages={656-674}
}
  • C. Kuehn
  • Published 2015
  • Mathematics, Computer Science, Physics
  • Appl. Math. Comput.
Numerical continuation calculations for ordinary differential equations (ODEs) are, by now, an established tool for bifurcation analysis in dynamical systems theory as well as across almost all natural and engineering sciences. Although several excellent standard software packages are available for ODEs, there are - for good reasons - no standard numerical continuation toolboxes available for partial differential equations (PDEs), which cover a broad range of different classes of PDEs… Expand
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References

SHOWING 1-10 OF 131 REFERENCES
pde2path - A Matlab package for continuation and bifurcation in 2D elliptic systems
  • 111
  • Highly Influential
  • PDF
Recipes for Continuation
  • 139
Algorithms and Visualization for solutions of nonlinear Elliptic equations
  • 106
  • PDF
On the numerical Continuation of Isolas of Equilibria
  • 8
  • PDF
A Minimax Method for Finding Multiple Critical Points and Its Applications to Semilinear PDEs
  • 98
  • PDF
MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs
  • 1,046
  • PDF
Deterministic Continuation of Stochastic Metastable Equilibria via Lyapunov Equations and Ellipsoids
  • C. Kuehn
  • Mathematics, Computer Science
  • SIAM J. Sci. Comput.
  • 2012
  • 23
  • PDF
...
1
2
3
4
5
...