zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On the numerical solution of stiff systems. (English) Zbl 1082.65545
Summary: We use power series method to solve stiff ordinary differential equations of the first order and an ordinary differential equation of any order by converting it into a system of differential of the order one. Theoretical considerations has been discussed and some examples were presented to show the ability of the method for linear and nonlinear systems of differential equations. We use MAPLE computer algebra systems for numerical calculations.

MSC:
65L05Initial value problems for ODE (numerical methods)
68W30Symbolic computation and algebraic computation
34A30Linear ODE and systems, general
34A34Nonlinear ODE and systems, general
Software:
Maple; RODAS
WorldCat.org
Full Text: DOI
References:
[1] Henrici, P.: Applied computational complex analysis. 1 (1974) · Zbl 0284.65001
[2] Corliss, G.; Chang, Y. F.: Solving ordinary differential equations using Taylor series. ACM trans. Math. soft. 8, 114-144 (1982) · Zbl 0503.65046
[3] Brenan, K. E.; Campbell, S. L.; Petzold, L. R.: Numerical solution of initial-value problems in differential-algebraic equations. (1989) · Zbl 0699.65057
[4] Hairer, E.; Wanner, G.: Solving ordinary differential equations II: Stiff and differential-algebreis problems. (1991) · Zbl 0729.65051
[5] Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T.: Numerical recipes. (1988)
[6] U.M. Ascher, L.R. Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2003. · Zbl 0908.65055
[7] Amodio, P.; Mazzia, F.: Numerical solution of differential-algebraic equations and computation of consistent initial/boundary conditions. J. comput. Appl. math. 87, 135-146 (1997) · Zbl 0894.65031
[8] Hull, T. E.; Enright, W. H.; Fellen, B. M.; Sedgwick, A. E.: Comparing numerical methods for ordinary differential equations. SIAM J. Numer. anal. 9, 603 (1972) · Zbl 0221.65115
[9] Frank, G.: Maple v. (1996)
[10] Çelik, E.; Karaduman, E.; Bayram, M.: Numerical method to solve chemical differential-algebraic equations. Int. J. Quant. chem. 89, No. 5, 447-451 (2002)
[11] Çelik, E.; Bayram, M.: Arbitrary order numerical method for solving differential-algebraic equation by Padé series. Appl. math. Comput. 137, 57-65 (2003) · Zbl 1031.65091