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math.NA2025
A Generalized Second-Order Positivity-Preserving Numerical Method for Non-Autonomous Dynamical Systems with Applications
Manh Tuan Hoang, Matthias Ehrhardt
In this work, we propose a generalized, second-order, nonstandard finite difference (NSFD) method for non-autonomous dynamical systems. The proposed method combines the NSFD framew…
math.NA2024
Absorbing Boundary Conditions for Variable Potential Schrödinger Equations via Titchmarsh-Weyl Theory
Matthias Ehrhardt, Chunxiong Zheng
We propose a novel approach to simulate the solution of the time-dependent Schrödinger equation with a general variable potential. The key idea is to approximate the Titchmarsh-Wey…
math.NA2023★ 1 cited
Deep smoothness WENO scheme for two-dimensional hyperbolic conservation laws: A deep learning approach for learning smoothness indicators
Tatiana Kossaczká, Ameya D. Jagtap, Matthias Ehrhardt
In this paper, we introduce an improved version of the fifth-order weighted essentially non-oscillatory (WENO) shock-capturing scheme by incorporating deep learning techniques. The…