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math.NA2026
Controlled B-series, controlled Runge-Kutta methods and controlled rough differential equations
Xinyuan An, Xingya Fan, Xing Gao
We develop controlled B-series and controlled Runge-Kutta methods as extensions of classical B-series and Runge-Kutta theory to controlled-driven rough differential equations. The…
math.NA2023
Sparse grid approximation of nonlinear SPDEs: The Landau--Lifshitz--Gilbert equation
Xin An, Josef Dick, Michael Feischl +2
We show convergence rates for a sparse grid approximation of the distribution of solutions of the stochastic Landau-Lifshitz-Gilbert equation. Beyond being a frequently studied equ…