zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Advanced type coupled matrix Riccati differential equation systems with Kronecker product. (English) Zbl 1193.34003
Summary: We consider a coupled matrix Riccati differential equation systems of advanced type, strongly coupled in its quadratic terms, and by the use of Kronecker products, we reduce it to an equation for which the successive method is applicable. Finally, we study an iterative scheme for solving the problem and obtaining the error bounds for the used scheme.

34A05Methods of solution of ODE
34K07Theoretical approximation of solutions of functional-differential equations
Full Text: DOI
[1] Barnett, S.: Matrix differential equations and Kronecker products. SIAM J. Appl. math. 24, 1-5 (1973) · Zbl 0252.34012
[2] Campbell, S.: Singular system of differential equations II. (1982) · Zbl 0482.34008
[3] Coddington, E. A.: An introduction to ordinary differential equations. (1968) · Zbl 0123.27301
[4] Jr., J. B. Cruz; Chen, C. I.: Series Nash solution of two-person non-zero sum linear differential games. J. optim. Theory appl. 7, No. 4, 240-257 (1971) · Zbl 0199.49004
[5] Jodar, L.; Kandil, H. A.: A resolution method for Riccati differential systems coupled in their quadratic terms. SIAM J. Math. anal. 19, 1425-1430 (1988) · Zbl 0663.65076
[6] Kandil, H. A.: Matrix Riccati equations in control and systems theory. (2003) · Zbl 1027.93001
[7] Ladas, G. E.; Laxmikantham, V.: Differential equations in abstract spaces. (1972)
[8] M. Mariton, Les systèm Linéaires à Sauts Markoviens, Thès d’Etat, Univ. Paris sud, Center d’Orasay, 1986.
[9] Starr, A. W.; Ho, Y. C.: Nonzero sum differential games. J. optim. Theory appl. 3, 184-206 (1969) · Zbl 0169.12301