Fourth-Order Time-Stepping for Stiff PDEs

By Aly-Khan Kassam, Lloyd N. Trefethen. 2005

1,074 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis

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Citations in the corpus

Fourierization of the Legendre--Galerkin method and a new space--time spectral method (2007, background): “As pointed out in [10], having diagonal mass and stiffness matrices is crucial in the implementation and analysis of some time-stepping schemes.”
Solving the nonlinear Schrodinger equation using exponential integrators (2006, background): “In evaluating -functions, Kassam & Trefethen (2005) discovered a stability problem which they solved by contour integral evaluation in the complex plane.”
TAYLOR EXPANSIONS OF SOLUTIONS OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH ADDITIVE NOISE (2010, neutral): “, [3-5, 16-19, 27, 30, 31, 36] ).”
Explicit Exponential Runge-Kutta Methods for Semilinear Parabolic Problems (2005, methodology): “Motivated by recent interest in exponential integrators for stiff problems [3] [9] [11] [12] and inspired by the promising numerical experiments reported in these papers, we present error bounds for a class of explicit exponential Runge-Kutta methods for semilinear parabolic problems u (t) + Au(t)…”
Finite difference methods for ordinary and partial differential equations - steady-state and time-dependent problems (2007, methodology): “See, for example, [8], [19], [48], [53] for more discussion of these methods.”
A Class of Explicit Exponential General Linear Methods (2006, methodology): “The explicit exponential Runge–Kutta methods considered in Hochbruck and Ostermann [11], see also [6, 7, 12, 13, 19], are contained in our method class (2.”
An ETD Crank‐Nicolson method for reaction‐diffusion systems (2012, methodology): “Du and Zhu [2], and Kassam and Trefethen [14], and Nie [7] pointed out some implementation difficulties.”
WEAK SINDY FOR PARTIAL DIFFERENTIAL EQUATIONS (2020, methodology): “A solution is obtained for (x, t) ∈ [0, 32π] × [0, 150] with periodic boundary conditions using ETDRK4 timestepping and Fourierspectral differentiation [9] with N1 = 256 points in space and N2 = 1500 points in time.”
An Asymptotic Parallel-in-Time Method for Highly Oscillatory PDEs (2013, background): “[20]), and Strang splitting (see Algorithm 3 of Section 3).”