Solving Ordinary Differential Equations in R

By Karline Soetaert, Jeff R. Cash, Francesca Mazzia. 2012

1,388 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/648d21c9cd26be2376516e8d0a70fff41f1246fe

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In Computational Theory and Mathematics

In Numerical Analysis

In Statistical and Nonlinear Physics

Citations in the corpus

micrOMEGAs4.1: Two dark matter candidates (2014, methodology): “In micrOMEGAs we use the Rosenbrock algorithm [36, 37] for solving stiff equations.”
FATODE: A Library for Forward, Adjoint, and Tangent Linear Integration of ODEs (2014, methodology): “1), as presented in the monograph [13, 14].”
Numerical and experimental study of the dynamics of a μs helium plasma gun discharge with various amounts of N2 admixture (2016, methodology): “Second, for the time integration of the detailed chemistry, we have used the implicit 5th order RADAU solver (Hairer and Wanner 1996).”
Multi-body dynamics simulation of geometrically exact Cosserat rods (2011, methodology): “Numerical approaches using local charts exist [29], however, changing charts is a tedious task and it is much easier to formulate the equations of motion as a system of differential algebraic equations, where we keep the quaternion unity condition 2g = ‖p‖2 − 1 = 0 as a hard algebraic constraint.”
ADI Schemes for Pricing American Options under the Heston Model (2013, methodology): “The penalty method is shown to yield the Heston LCP as the penalty parameter tends to infinity. Ikonen and Toivanen (2007) propose splitting methods for the time discretization of the semidiscretized Heston PDCP.”
Stochastic Normalizing Flows (2020, background): “Adaptive solvers prove particularly eﬀective, although, as pointed out in Gholami et al. (2019), the backward solve (4) can often run into stability issues, suggesting a Rosenbrock or other implicit approach (Hairer & Wanner, 1996).”
MODULES FOR EXPERIMENTS IN STELLAR ASTROPHYSICS (MESA): PLANETS, OSCILLATIONS, ROTATION, AND MASSIVE STARS (2013, positive): “The MESA one-zone burn routines now include user-specified options for the family of stiff ordinary differential equation integrators from Hairer & Wanner (1996).”
Unifying time evolution and optimization with matrix product states (2014, background): “More concretely, the TDVP equations suffer from what is known as stiffness in the numerical analysis literature [20] and this results in a severe stepsize restriction when using standard explicit time integrators.”
An analysis of the spectrum of the discontinuous Galerkin method (2013, background): “12 in [10], which states that the curve |R(z)| = 1, whereR(z) is the[p/p+1] Padé approximant ofexp(z) is located in the right half of the complex plane.”