
Accession Number : ADA300491
Title : TimeAdvance Algorithms Based on Hamilton's Principle.
Descriptive Note : Final technical rept. 1 Aug 9230 Sep 95,
Corporate Author : DARTMOUTH COLL HANOVER NH DEPT OF PHYSICS AND ASTRONOMY
Personal Author(s) : Lewis, H. R. ; Kostelec, Peter J. ; Shepherd, Simon G.
PDF Url : ADA300491
Report Date : 30 SEP 1995
Pagination or Media Count : 9
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 VlasovMaxwell 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 timeadvance algorithms were identified analytically and by numerical comparison with other methods, such as RungeKutta and symplectic algorithms. This approach to time advance can be extended to include partial differential equations and the VlasovMaxwell equations. Application has been made to derive a secondorder accurate algorithm for the linear wave equation; the dispersive properties of the algorithm are superior to those of the usual secondorder accurate explicit or implicit algorithms.
Descriptors : *ALGORITHMS, *PLASMAS(PHYSICS), *MAXWELLS EQUATIONS, *LAGRANGIAN FUNCTIONS, OPTIMIZATION, TIME DEPENDENCE, COMPARISON, APPROXIMATION(MATHEMATICS), POLYNOMIALS, INTERPOLATION, PARTIAL DIFFERENTIAL EQUATIONS, NUMERICAL METHODS AND PROCEDURES, TIME DOMAIN, VARIATIONAL PRINCIPLES, HAMILTONIAN FUNCTIONS, WAVE EQUATIONS, LINEAR DIFFERENTIAL EQUATIONS.
Subject Categories : Numerical Mathematics
Plasma Physics and Magnetohydrodynamics
Distribution Statement : APPROVED FOR PUBLIC RELEASE