Accession Number : ADA300491

Title :   Time-Advance Algorithms Based on Hamilton's Principle.

Descriptive Note : Final technical rept. 1 Aug 92-30 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 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.

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