Symplectic phase flow approximation for the numerical integration of canonical systems
Numerische MathematikPublished 1 December 1992
Stefan Miesbach, Hans Josef Pesch
Citations17
SJR quartileQ1
SJR score1.64
SNIP1.57
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Abstract
New methods are presented for the numerical integration of ordinary differential equations of the important family of Hamiltonian dynamical systems. These methods preserve the Poincaré invariants and, therefore, mimic relevant qualitative properties of the exact solutions. The methods are based on a Runge-Kutta-type ansatz for the generating function to realize the integration steps by canonical transformations. A fourth-order method is given and its implementation is discussed. Numerical results are presented for the Hénon-Heiles system, which describes the motion of a star in an axisymmetric galaxy.
Keywords
MathematicsPhysics and Astronomy
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