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Energy and Momentum Conserving Methods of Arbitrary Order For the Numerical Integration of Equations of Motion. I. Motion of a Single Particle
(University of Wisconsin-Madison Department of Computer Sciences, 1974)
Conventional numerical methods, when applied to the ordinary differential equations of motion of classical mechanics, conserve the total energy and angular momentum only to the order of the truncation error. Since these ...
Discrete Mechanics - A General Treatment
(University of Wisconsin-Madison Department of Computer Sciences, 1973)
A new numerical method for use in the solution of classical equations of motion is described, accurate to third-order in the coordinates and second-order in the velocities. The method has the unique property of preserving ...