Pryce Structural Analysis Adapted to Hermite—Birkhoff—Taylor DAE Solvers
Abstract
The ODE solver HBT(12)5 of order 12 (Appl. Math. Comput., 211, 313328 (2009)), which combines a Taylor series method of order 9 with a Runge—Kutta method of order 4, is expanded into the DAE solver HBT(12)5DAE of order 12. Pryce structural preanalysis, extended ODEs and ODE firstorder forms are adapted to HBT(12)5DAE with a stepsize control based on local error estimators and a modified Pryce algorithm to advance integration. HBT(12)5DAE uses only the first nine derivatives of the unknown variables as opposed to the first 12 derivatives used by the Taylor series method of order 12 for DAEs.
 Publication:

Advances in Mathematical and Computational Methods: Addressing Modern Challenges of Science, Technology, and Society
 Pub Date:
 November 2011
 DOI:
 10.1063/1.3663514
 Bibcode:
 2011AIPC.1368..283N
 Keywords:

 error analysis;
 integration;
 initial value problems;
 problem solving;
 06.20.Dk;
 02.30.Cj;
 04.20.Ex;
 02.60.Cb;
 Measurement and error theory;
 Measure and integration;
 Initial value problem existence and uniqueness of solutions;
 Numerical simulation;
 solution of equations