Splitting methods

By Robert I. McLachlan, G. Quispel. Acta Numerica, 2002

814 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/6b65572cd538c7fb9c88e6c5f7ef1862427373c9

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In Numerical Analysis

Citations in the corpus

Multisymplectic box schemes and the Korteweg{de Vries equation (2004, methodology): “Our first method is a semi-explicit splitting method [15].”
Nonintrusive and Structure Preserving Multiscale Integration of Stiff ODEs, SDEs, and Hamiltonian Systems with Hidden Slow Dynamics via Flow Averaging (2009, neutral): “…the first and last steps) iterating Θδ defined by (2.7) is equivalent to iterating Θδ := Φ 0,∗ δ−τ 2 ◦ Φ0δ−τ 2 ◦ Φ 1 τ 2 ◦ Φ 1 ,∗ τ 2 (2.8) It follows that a symplectic, symmetric and reversible FLAVOR can be obtained in a nonintrusive way from a Störmer/Verlet integrator for (2.1) [53, 55, 114].”
On the necessity of negative coefficients for operator splitting schemes of order higher than two (2005, methodology): “As a consequence, by considering both the kernel ψh and the post-processor πh as compositions of basic integrators, highly efficient processed methods have been proposed [23,2,1,17].”
Geometric integrators for ODEs (2006, methodology): “In some cases (as in some types of structured matrices and some classes of differential equations) it can be impossible to preserve the given structure [38], while in others it is unknown whether or not such a method exists ([83], §6).”
High order splitting methods for analytic semigroups exist (2009, background): “Contemporary surveys addressing the usage of exponential splitting meth ods can be found in [6,10, 11].”
Understanding and Improving Transformer From a Multi-Particle Dynamic System Point of View (2019, methodology): “The splitting method is a prevailing way of solving such coupled differential equations that can be decomposed into a sum of differential operators [23].”
The Magnus expansion and some of its applications (2008, methodology): “dependently in areas of research as diverse as celestial mechanics, molecular dynamics, control theory, particle accelerators physics, and numerical analysis [99,119,146,165,166].”
Geometric numerical integration illustrated by the Störmer–Verlet method (2003, methodology): “For a careful survey of splitting methods we refer to McLachlan and Quispel (2002).”