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pro vyhledávání: '"65m70"'
We prove a nearly optimal error bound on the exponential wave integrator Fourier spectral (EWI-FS) method for the logarithmic Schr\"odinger equation (LogSE) under the assumption of $H^2$-solution, which is theoretically guaranteed. Subject to a CFL-t
Externí odkaz:
http://arxiv.org/abs/2412.16902
Shallow water equations (SWE) are fundamental nonlinear hyperbolic PDE-based models in fluid dynamics that are essential for studying a wide range of geophysical and engineering phenomena. Therefore, stable and accurate numerical methods for SWE are
Externí odkaz:
http://arxiv.org/abs/2412.16353
We construct fully-discrete schemes for the Benjamin-Ono, Calogero-Sutherland DNLS, and cubic Szeg\H{o} equations on the torus, which are $\textit{exact in time}$ with $\textit{spectral accuracy}$ in space. We prove spectral convergence for the first
Externí odkaz:
http://arxiv.org/abs/2412.13480
In this paper, we focus on efficiently and flexibly simulating the Fokker-Planck equation associated with the Nonlinear Noisy Leaky Integrate-and-Fire (NNLIF) model, which reflects the dynamic behavior of neuron networks. We apply the Galerkin spectr
Externí odkaz:
http://arxiv.org/abs/2412.10676
In recent years, stochastic effects have become increasingly relevant for describing fluid behaviour, particularly in the context of turbulence. The most important model for inviscid fluids in computational fluid dynamics are the Euler equations of g
Externí odkaz:
http://arxiv.org/abs/2412.07613
Understanding the nanoscale effects controlling the dynamics of a contact line -- defined as the line formed at the junction of two fluid phases and a solid -- has been a longstanding problem in fluid mechanics pushing experimental and numerical meth
Externí odkaz:
http://arxiv.org/abs/2412.05643
The degrees of freedom of Active Flux are cell averages and point values along the cell boundaries. These latter are shared between neighbouring cells, which gives rise to a globally continuous reconstruction. The semi-discrete Active Flux method use
Externí odkaz:
http://arxiv.org/abs/2412.03477
Two primary scalar auxiliary variable (SAV) approaches are widely applied for simulating gradient flow systems, i.e., the nonlinear energy-based approach and the Lagrange multiplier approach. The former guarantees unconditional energy stability throu
Externí odkaz:
http://arxiv.org/abs/2411.17403
In this work, we develop a class of up to third-order energy-stable schemes for the Cahn--Hilliard equation. Building on Lawson's integrating factor Runge--Kutta method, which is widely used for stiff semilinear equations, we discuss its limitations,
Externí odkaz:
http://arxiv.org/abs/2411.16271
The a priori error analysis of reduced order models (ROMs) for fluids is relatively scarce. In this paper, we take a step in this direction and conduct numerical analysis of the recently introduced time relaxation ROM (TR-ROM), which uses spatial fil
Externí odkaz:
http://arxiv.org/abs/2411.08986