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Increment formulations for rounding error reduction in the numerical solution of structured differential systems

Mark Sofroniou
Organization: Wolfram Research, Inc.
Department: Kernel Technology
G. Spaletta
Organization: Bologna University
Department: Mathematics Dept
Journal / Anthology

Future Generation Computer Systems
Year: 2003
Volume: 19
Issue: 3
Page range: 375--83

Strategies for reducing the effect of cumulative rounding errors in geometric numerical integration are outlined. The focus is, in particular, on the solution of separable Hamiltonian systems using explicit symplectic integration methods and on solving orthogonal matrix differential systems using projection. Examples are given that demonstrate the advantages of an increment formulation over the standard implementation of conventional integrators. We describe how the aforementioned special purpose integration methods have been set up in a uniform, modular and extensible framework being developed in the problem solving environment Mathematica.

*Mathematics > Calculus and Analysis > Differential Equations

Geometric numerical integration, Separable Hamiltonian differential equations, Symplectic methods, Composition methods, Orthogonal projection