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- John M. Neuberger, James W. Swift
- I. J. Bifurcation and Chaos
- 2001

In this paper we primarily consider the family of elliptic PDEs âˆ†u+ f(u) = 0 on the square region Î© = (0, 1)Ã— (0, 1) with zero Dirichlet boundary condition. Following our previous analysis andâ€¦ (More)

- James W. Swift, Ã‰.
- 2002

This paper describes the process of pattern selection between rolls and hexagons in Rayleigh-l~nard convection with reflectional symmetry in the horizontal midplane. This symmetry is a consequence ofâ€¦ (More)

- John M. Neuberger, NÃ¡ndor Sieben, James W. Swift
- I. J. Bifurcation and Chaos
- 2009

We seek solutions u âˆˆ R n to the semilinear elliptic partial difference equation âˆ’Lu + fs(u) = 0, where L is the matrix corresponding to the Laplacian operator on a graph G and fs is a one-parameterâ€¦ (More)

- John M. Neuberger, NÃ¡ndor Sieben, James W. Swift
- SIAM J. Applied Dynamical Systems
- 2006

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 aâ€¦ (More)

- John M. Neuberger, NÃ¡ndor Sieben, James W. Swift
- International Journal of Parallel Programming
- 2012

We present a simple and easy to apply methodology for using high-level self-submitting parallel job queues in an MPI environment. Using C++, we implemented a library of functions, MPQueue, both forâ€¦ (More)

- John M. Neuberger, Dennis R. Rice, James W. Swift
- I. J. Bifurcation and Chaos
- 2003

We numerically compute solutions to the vector Ginzburg-Landau equation with a triple-well potential. We use the Galerkin Newton Gradient Algorithm of Neuberger & Swift and bifurcation techniques toâ€¦ (More)

We derive the averaged equations describing a series array of Josephson junctions shunted by a parallel inductor-resistor-capacitor load. We assume that the junctions have negligable capacitance (Î² =â€¦ (More)

- C. TYLER DIGGANS, John M. Neuberger, James W. Swift
- 2013

We study a two-parameter family of so-called Hamiltonian systems defined on a region Î© in R with the bifurcation parameters Î» and Î¼ of the form: âˆ†u+ âˆ‚ âˆ‚v HÎ»,Î¼(u, v) = 0 âˆ†v + âˆ‚ âˆ‚u HÎ»,Î¼(u, v) = 0 on Î©,â€¦ (More)

We show how the symmetry of attractors of equivariant dynamical systems can be observed by equivariant projections of the phase space. Equivariant projections have long been used, but they can giveâ€¦ (More)

- John M. Neuberger, NÃ¡ndor Sieben, James W. Swift
- SIAM J. Applied Dynamical Systems
- 2013

We seek discrete approximations to solutions u : Î© â†’ R of semilinear elliptic partial differential equations of the form âˆ†u+ fs(u) = 0, where fs is a one-parameter family of nonlinear functions and Î©â€¦ (More)

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