Some practical Runge-Kutta formulas

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FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models (2018, methodology): “In all experiments the Runge-Kutta 4(5) algorithm with the tableau from Shampine (1986) was used to solve the ODEs.”
Low-storage, Explicit Runge-Kutta Schemes for the Compressible Navier-Stokes Equations (2000, unknown): “In comparing schemes with different orders of accuracy we cannot use this last metric and simply paraphrase Shampine [71].”
Bespoke Solvers for Generative Flow Models (2023, methodology): “Ground Truth (GT) sample trajectories, x ( t i ) , are computed with an adaptive RK45 solver (Shampine, 1986).”
Scalable Reversible Generative Models with Free-form Continuous Dynamics (2018, methodology): “In all experiments the Runge-Kutta 4(5) algorithm with the tableau from Shampine (1986) was used to solve the ODEs.”
Neural Networks with Cheap Differential Operators (2019, methodology): “We compare a standard Runge-Kutta (RK) solver with adaptive stepping (Shampine, 1986) and a predictor-corrector Adams-Bashforth-Moulton (ABM) method in Figure 2.”
Continuous Newton's Method for Power Flow Analysis (2009, background): “An interesting discussion on the Runge–Kutta truncation error estimation can be found in [ 33 ].”
Learning Differential Equations that are Easy to Solve (2020, methodology): “Unless speciﬁed otherwise, we use the standard dopri5 Runge-Kutta 4(5) solver (Dormand & Prince, 1980; Shampine, 1986).”