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math.NA2022
Stability of structure-aware Taylor methods for tents
Jay Gopalakrishnan, Zheng Sun
Structure-aware Taylor (SAT) methods are a class of timestepping schemes designed for propagating linear hyperbolic solutions within a tent-shaped spacetime region. Tents are usefu…
math.NA2022
On Energy Laws and Stability of Runge--Kutta Methods for Linear Seminegative Problems
Zheng Sun, Yuanzhe Wei, Kailiang Wu
This paper presents a systematic theoretical framework to derive the energy identities of general implicit and explicit Runge--Kutta (RK) methods for linear seminegative systems. I…