Composed BDF schemes with complex coefficients increase order by one, supply order p+1 error estimates from the imaginary part, break the Dahlquist barrier up to order 8, and give step-ratio stability bounds for non-uniform meshes.
Journal of Computational Physics , volume =
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SGNO achieves stable long-horizon PDE rollouts by organizing autoregressive steps as spectral evolution updates with a constrained diagonal generator and learned correction, delivering a median 74.8% reduction in GMean100 error across ten APEBench tasks.
Quantized local reduced-order models paired with adjoint optimization reconstruct full trajectories in the chaotic Kuramoto-Sivashinsky equation up to 0.25 Lyapunov times with 3.5x speedup over full-order models.
Simulations demonstrate non-monotonic guide-field regulation of reconnection efficiency via balance between drift-kink suppression and tearing-mode hindrance in 3D relativistic current sheets.
citing papers explorer
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Error estimation for numerical approximations of ODEs via composition techniques. Part II: BDF methods
Composed BDF schemes with complex coefficients increase order by one, supply order p+1 error estimates from the imaginary part, break the Dahlquist barrier up to order 8, and give step-ratio stability bounds for non-uniform meshes.
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SGNO: Spectral Generator Neural Operators for Stable Long Horizon PDE Rollouts
SGNO achieves stable long-horizon PDE rollouts by organizing autoregressive steps as spectral evolution updates with a constrained diagonal generator and learned correction, delivering a median 74.8% reduction in GMean100 error across ten APEBench tasks.
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Adjoint-based optimization with quantized local reduced-order models for spatiotemporally chaotic systems
Quantized local reduced-order models paired with adjoint optimization reconstruct full trajectories in the chaotic Kuramoto-Sivashinsky equation up to 0.25 Lyapunov times with 3.5x speedup over full-order models.
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Guide-Field-mediated Multiscale Instabilities in Relativistic Reconnection
Simulations demonstrate non-monotonic guide-field regulation of reconnection efficiency via balance between drift-kink suppression and tearing-mode hindrance in 3D relativistic current sheets.