9 Result(s)
within
Jan Bouwe van den Berg
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Article
Validated integration of semilinear parabolic PDEs
Integrating evolutionary partial differential equations (PDEs) is an essential ingredient for studying the dynamics of the solutions. Indeed, simulations are at the core of scientific computing, but their math...
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Validated Numerical Approximation of Stable Manifolds for Parabolic Partial Differential Equations
This paper develops validated computational methods for studying infinite dimensional stable manifolds at equilibrium solutions of parabolic PDEs, synthesizing disparate errors resulting from numerical approxi...
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Toward Computational Morse–Floer Homology: Forcing Results for Connecting Orbits by Computing Relative Indices of Critical Points
To make progress toward better computability of Morse–Floer homology and thus enhance the applicability of Floer theory, it is essential to have tools to determine the relative index of equilibria. Since even ...
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Article
Open AccessLarge Fronts in Nonlocally Coupled Systems Using Conley–Floer Homology
In this paper, we study travelling front solutions for nonlocal equations of the type $$\begin{aligned} \partial _t u = N * S(u) + \nabla F(u)...
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A General Method for Computer-Assisted Proofs of Periodic Solutions in Delay Differential Problems
In this paper we develop a general computer-assisted proof method for periodic solutions to delay differential equations. The class of problems considered includes systems of delay differential equations with ...
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Spontaneous Periodic Orbits in the Navier–Stokes Flow
In this paper, a general method to obtain constructive proofs of existence of periodic orbits in the forced autonomous Navier–Stokes equations on the three-torus is proposed. After introducing a zero finding p...
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Article
Open AccessComputing (Un)stable Manifolds with Validated Error Bounds: Non-resonant and Resonant Spectra
We develop techniques for computing the (un)stable manifold at a hyperbolic equilibrium of an analytic vector field. Our approach is based on the so-called parametrization method for invariant manifolds. A fea...
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Article
The Interplay Between Scent Trails and Group-Mass Recruitment Systems in Ants
Large ant colonies invariably use effective scent trails to guide copious ant numbers to food sources. The success of mass recruitment hinges on the involvement of many colony members to lay powerful trails. H...
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Open AccessClosed characteristics on non-compact hypersurfaces in \({\mathbb {R}^{2n}}\)
Viterbo demonstrated that any (2n − 1)-dimensional compact hypersurface \({M \subset (\mathbb {R}^{2n},\omega)}\) of contact ty...
