119 citations · 139 across the 12 of their papers we have counts for
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math.DS2010
Automated Bifurcation Analysis for Nonlinear Elliptic Partial Difference Equations on Graphs
John M. Neuberger, Nandor Sieben, James W. Swift
We seek solutions to the semilinear elliptic partial difference equation , where is the matrix corresponding to the Laplacian operator on a graph $…
math.DS2010★ 11 cited
Symmetry and Automated Branch Following for a Semilinear Elliptic PDE on a Fractal Region
John M. Neuberger, Nandor Sieben, James W. Swift
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 sn…
math.DS2010
Computing Eigenfunctions on the Koch Snowflake: A New Grid and Symmetry
John M. Neuberger, Nandor Sieben, James W. Swift
In this paper we numerically solve the eigenvalue problem on the fractal region defined by the Koch Snowflake, with zero-Dirichlet or zero-Neumann boundary conditions…