107 citations · 1.1k across the 120 of their papers we have counts for
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A numerical stability investigation of strong ZND detonations for Majda's model
Blake Barker, Kevin zumbrun
We carry out a systematic numerical stability analysis of ZND detonations of Majda's model with Arrhenius-type ignition function, a simplified model for reacting flow, as heat rele…
Efficient numerical stability analysis of detonation waves in ZND
Jeffrey Humpherys, Kevin Zumbrun
As described in the classic works of Lee--Stewart and Short--Stewart, the numerical evaluation of linear stability of planar detonation waves is a computationally intensive problem…
Convergence of Hill's method for nonselfadjoint operators
Mathew A. Johnson, Kevin Zumbrun
By the introduction of a generalized Evans function defined by an appropriate 2-modified Fredholm determinant, we give a simple proof of convergence in location and multiplicity of…
Numerical error analysis for Evans function computations: a numerical gap lemma, centered-coordinate methods, and the unreasonable effectiveness of continuous orthogonalization
Kevin Zumbrun
We perform error analyses explaining some previously mysterious phenomena arising in numerical computation of the Evans function, in particular (i) the advantage of centered coordi…
A local greedy algorithm and higher order extensions for global numerical continuation of analytically varying subspaces
Kevin Zumbrun
We present a family of numerical implementations of Kato's ODE propagating global bases of analytically varying invariant subspaces, of which the first-order version is a surprisin…
An efficient shooting algorithm for Evans function calculations in large systems
Jeffrey Humpherys, Kevin Zumbrun
In Evans function computations of the spectra of asymptotically constant-coefficient linear operators, a basic issue is the efficient and numerically stable computation of subspace…