Explicit Exponential Runge-Kutta Methods for Semilinear Parabolic Problems

By Marlis Hochbruck, Alexander Ostermann. 2005

503 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis

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Citations in the corpus

DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps (2022, methodology): “The proposed solvers and analysis are highly motivated by the methods of exponential integrators [25, 31] in the ODE literature.”
Solving the nonlinear Schrodinger equation using exponential integrators (2006, methodology): “A recent paper of Hochbruck and Ostermann [9] studies exponential integrators applied to infinite dimensional semi-linear parabolic Cauchy problems.”
UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models (2023, methodology): “For any non-zero sequence { r i } =1 and h > 0 define , where φ n ( h ) is defined by the recursive relation [16]: For an increasing sequence where | · | denotes the l 1 norm for matrix.”
Fourth-and sixth-order commutator-free Magnus integrators for linear and non-linear dynamical systems (2006, background): “and for which efficient (possibly Runge–Kutta) exponential integrators for the autonomous problem are known (see [ 15 ,28] and references therein for more information on exponential integrators).”
TAYLOR EXPANSIONS OF SOLUTIONS OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH ADDITIVE NOISE (2010, unknown): “, [3-5, 16-19, 27, 30, 31, 36] ).”
A Class of Explicit Exponential General Linear Methods (2006, methodology): “In this paper, we study a class of explicit exponential general linear methods that in particular contains the exponential Runge–Kutta methods and the exponential Adams-type methods considered recently in the literature, see [3, 6, 11, 12, 13] and further [5].”
An ETD Crank‐Nicolson method for reaction‐diffusion systems (2012, methodology): “We now need to examine how to extend their proof [3] for (1,1)-Padé discretization of these matrix exponentials.”
Numerical Methods for Evolutionary Differential Equations (2008, methodology): “Of course an appropriately fast method for evaluating the exponential function, or more precisely ez for any given vector z, is crucial to the performance of methods based on this approach [135, 94, 95].”
Exponential Runge--Kutta methods for parabolic problems (2005, methodology): “In our paper [10], we have analyzed the convergence properties of such explicit exponential methods for semilinear parabolic problems.”