Stability analysis of reducible quadrature methods for Volterra integro-differential equations
Vernon L. Bakke; Zdzisław Jackiewicz
Aplikace matematiky (1987)
- Volume: 32, Issue: 1, page 37-48
- ISSN: 0862-7940
Access Full Article
top
Abstract
topHow to cite
topBakke, Vernon L., and Jackiewicz, Zdzisław. "Stability analysis of reducible quadrature methods for Volterra integro-differential equations." Aplikace matematiky 32.1 (1987): 37-48. <http://eudml.org/doc/15478>.
@article{Bakke1987,
abstract = {Stability analysis for numerical solutions of Voltera integro-differential equations based on linear multistep methods combined with reducible quadrature rules is presented. The results given are based on the test equation $y^\{\prime \}(t)=\gamma y(t) + \int ^t_0(\lambda + \mu t + vs) y(s) ds$ and absolute stability is deffined in terms of the real parameters $\gamma , \lambda , \mu $ and $v$. Sufficient conditions are illustrated for $(0;0)$ - methods and for combinations of Adams-Moulton and backward differentiation methods.},
author = {Bakke, Vernon L., Jackiewicz, Zdzisław},
journal = {Aplikace matematiky},
keywords = {backward-differentiation-formula method; Volterra integro-differential equations; theta method; test equation; stability; linear multistep methods; reducible quadrature formulas; linear difference equation; Adams-Moulton methods; stability of numerical solution; backward-differentiation-formula method; Volterra integro-differential equations; theta method; test equation; stability; linear multistep methods; reducible quadrature formulas; linear difference equation; Adams-Moulton methods},
language = {eng},
number = {1},
pages = {37-48},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Stability analysis of reducible quadrature methods for Volterra integro-differential equations},
url = {http://eudml.org/doc/15478},
volume = {32},
year = {1987},
}
TY - JOUR
AU - Bakke, Vernon L.
AU - Jackiewicz, Zdzisław
TI - Stability analysis of reducible quadrature methods for Volterra integro-differential equations
JO - Aplikace matematiky
PY - 1987
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 32
IS - 1
SP - 37
EP - 48
AB - Stability analysis for numerical solutions of Voltera integro-differential equations based on linear multistep methods combined with reducible quadrature rules is presented. The results given are based on the test equation $y^{\prime }(t)=\gamma y(t) + \int ^t_0(\lambda + \mu t + vs) y(s) ds$ and absolute stability is deffined in terms of the real parameters $\gamma , \lambda , \mu $ and $v$. Sufficient conditions are illustrated for $(0;0)$ - methods and for combinations of Adams-Moulton and backward differentiation methods.
LA - eng
KW - backward-differentiation-formula method; Volterra integro-differential equations; theta method; test equation; stability; linear multistep methods; reducible quadrature formulas; linear difference equation; Adams-Moulton methods; stability of numerical solution; backward-differentiation-formula method; Volterra integro-differential equations; theta method; test equation; stability; linear multistep methods; reducible quadrature formulas; linear difference equation; Adams-Moulton methods
UR - http://eudml.org/doc/15478
ER -
References
top- С. T. H. Baker A. Makroglou E. Short, Regions of stability in the numerical treatment of Volterra integro-differential equations, SIAM J. Numer. Anal., Vol. 16, No. 6, December, 1979. (1979) MR0551314
- V. L. Bakke Z. Jackiewicz, 10.1007/BF01389707, Numer. Math. 47 (1985), 159-173. (1985) MR0799682DOI10.1007/BF01389707
- V. L. Bakke Z. Jackiewicz, 10.1016/0022-247X(86)90018-1, J. Math. Anal. Appl., 115 (1986), 592-605. (1986) MR0836249DOI10.1016/0022-247X(86)90018-1
- H. Brunner, A survey of recent advances in the numerical treatment of Volterra integral and integro-differential equations, J. Comput. App. Math., Vol. 8, No. 3, 1982. (1982) Zbl0485.65087MR0682889
- H. Brunner J. D. Lambert, 10.1007/BF02239501, Computing 12, 75-89 (1974). (1974) MR0418490DOI10.1007/BF02239501
- C. J. Gladwin R. Jeltsch, 10.1007/BF01932943, BIT 14, 144-151 (1974). (1974) MR0502108DOI10.1007/BF01932943
- P. Linz, 10.1145/321510.321521, J. Assoc. Comput. Mach., 16 (1969), 295-301. (1969) Zbl0183.45002MR0239786DOI10.1145/321510.321521
- J. Matthys, 10.1007/BF01399087, Numer. Math. 27, 85-94 (1976). (1976) Zbl0319.65072MR0436638DOI10.1007/BF01399087
- D. Sanchez, A short note on asymptotic estimates of stability regions for a certain class of Volterra integro-differential equations, Manuscript, Department of Mathematics and Statistics, University of New Mexico, May, 1984. (1984)
- L. M. Milne-Thompson, The calculus of finite differences, MacMillan& Co., London, 1933. (1933)
- P. H. M. Wolkenfelt, 10.1093/imanum/2.2.131, IMA Journal of Numerical Analysis, 2, 131-152 (1982). (1982) Zbl0481.65084MR0668589DOI10.1093/imanum/2.2.131
- P. H. M. Wolkenfelt, 10.1002/zamm.19810610808, Z. Angew. Math. Mech., 61, 399-401 (1981). (1981) Zbl0466.65073MR0638029DOI10.1002/zamm.19810610808
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.