Structure-Preserving Integration Algorithms [report]

B. A. Shadwick, W. F. Buell, J. C. Bowman
2000 unpublished
Often in physics and engineering one encounters systems of differential equations that have a non-trivial dynamic or kinematic structure, e.g., the flow generated by such a system may satisfy one or more algebraic or differential constraints. Moreover, this structure is often of physical significance, embodying an important concept such as conservation of energy. Traditional numerical methods for solving initial value problems typically do not preserve any structure possessed by the system and
more » ... by the system and can be computationally less efficient than algorithms specifically designed to honour a system's structure. Also of interest are "near ideal" systems, where some conservation property is only weakly violated. Through a series of examples drawn from various physical systems, we discuss numerical algorithms which, in each case, are specifically constructed to preserve the structure of the system under consideration. These methods are shown to be of particular interest when the integration interval is significantly longer than the characteristic time scale(s) of the system.
doi:10.21236/ada384935 fatcat:tacnqwkcgrgthnxuhw7t6ltik4