Time-Advance Algorithms Based on Hamilton's Principle.
Abstract
Hamilton's principle was applied to derive a class of numerical algorithms for systems of ordinary differential equations when the equations are derivable from a Lagrangian. This is an important extension into the time domain of an earlier use of Hamilton's principle to derive algorithms for the spatial operators in Maxwell's equations. In that work, given a set of expansion functions for spatial dependences, the Vlasov-Maxwell equations were replaced by a system of ordinary differential equations in time; but the question of solving the ordinary differential equations was not addressed. Advantageous properties of the new time-advance algorithms were identified analytically and by numerical comparison with other methods, such as Runge-Kutta and symplectic algorithms. This approach to time advance can be extended to include partial differential equations and the Vlasov-Maxwell equations. Application has been made to derive a second-order accurate algorithm for the linear wave equation; the dispersive properties of the algorithm are superior to those of the usual second-order accurate explicit or implicit algorithms.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 30, 1995
- Accession Number
- ADA300491
Entities
People
- H. R. Lewis
- Peter J. Kostelec
- Simon Shepherd
Organizations
- Dartmouth College