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Backward Error Analysis For Numerical Integrators

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Applied Mathematics Philadelphia, PA, USA tableofcontents doi>10.1137/S0036142997329797 1999 Article Bibliometrics ·Downloads (6 Weeks): 0 ·Downloads (12 Months): 0 ·Downloads (cumulative): 0 ·Citation Count: 19 Recent authors with related interests Concepts in this article powered by Concepts inBackward Error Analysis for Numerical Integrators Numerical methods for ordinary differential equations Numerical ordinary differential equations is the part of numerical analysis which studies the numerical solution of ordinary differential equations (ODEs). This field is also known under the name numerical integration, but some http://epubs.siam.org/doi/abs/10.1137/S0036142997329797 people reserve this term for the computation of integrals. Many differential equations cannot be solved analytically; however, in science and engineering, a numeric approximation to the solution is often good enough to solve a problem. morefromWikipedia Symplectic integrator In mathematics, a symplectic integrator (SI) is a numerical integration scheme for a specific group of differential equations related to http://dl.acm.org/citation.cfm?id=333895 classical mechanics and symplectic geometry. Symplectic integrators form the subclass of geometric integrators which, by definition, are canonical transformations. They are widely used in molecular dynamics, discrete element methods, accelerator physics, and celestial mechanics. morefromWikipedia Hamiltonian system In physics and classical mechanics, a Hamiltonian system is a physical system in which forces are momentum invariant. Hamiltonian systems are studied in Hamiltonian mechanics. In mathematics, a Hamiltonian system is a system of differential equations which can be written in the form of Hamilton's equations. Hamiltonian systems are usually formulated in terms of Hamiltonian vector fields on a symplectic manifold or Poisson manifold. Hamiltonian systems are a special case of dynamical systems. morefromWikipedia Taylor's theorem In calculus, Taylor's theorem gives an approximation of a k times differentiable function around a given point by a k-th order Taylor-polynomial. For analytic functions the Taylor polynomials at a given point are finite order truncations of its Taylor's series, which completely determines the function in some neighborhood of the point. The exact content of "Taylor's theorem" is not universally agre

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