ISSN:
1572-9265
Keywords:
Multistep methods
;
differential-algebraic equations
;
stability
;
existence and uniqueness
;
convergence of iterative method
;
65L06
;
65L20
;
65N22
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract Multistep methods for the differential/algebraic equations (DAEs) in the form of $$F_1 (x) = 0, F_2 (x,x',z) = 0$$ are presented, whereF 1 maps from ℝ n to ℝ ′ ,F 2 from ℝ n x ℝ n x ℝ m to ℝ s andr〈n≤r+s=n+m. By employing the deviations of the available existence theories, a new form of the multistep method for solutions of (1) is developed. Furthermore, it is shown that this method has no typical instabilities such as those that may occur in the application of multistep method to DAEs in the traditional manner. A proof of the solvability of the multistep system is provided, and an iterative method is developed for solving these nonlinear algebraic equations. Moreover, a proof of the convergence of this iterative method is presented.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02140771
