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

Abstract

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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 ' ( t ) = γ y ( t ) + ∫ 0 t ( λ + μ t + v s ) y ( s ) d s and absolute stability is deffined in terms of the real parameters γ , λ , μ and v . Sufficient conditions are illustrated for ( 0 ; 0 ) - methods and for combinations of Adams-Moulton and backward differentiation methods.

How to cite

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Bakke, 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

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  9. 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) 
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  11. 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
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