ISSN:
0945-3245
Keywords:
AMS(MOS): 65L05
;
CR: G1.7
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary This paper deals with the numerical solution of Differential/Algebraic Equations (DAE) of index one. It begins with the development of a general theory on the Taylor expansion for the exact solutions of these problems, which extends the well-known theory of Butcher for first order ordinary differential equations to DAE's of index one. As an application, we obtain Butcher-type results for Rosenbrock methods applied to DAE's of index one, we characterize numerical methods as applications of certain sets of trees. We derive convergent embedded methods of order 4(3) which require 4 or 5 evaluations of the functions, 1 evaluation of the Jacobian and 1 LU factorization per step.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01401021
Permalink
