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Stability of Numerical Methods for Volterra Integro‐Differential Equations of Convolution Type
Author(s) -
Bakke V. L.,
Jackiewicz Z.
Publication year - 1988
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19880680210
Subject(s) - convolution (computer science) , mathematics , stability (learning theory) , volterra integral equation , differential equation , volterra equations , numerical stability , integro differential equation , type (biology) , mathematical analysis , numerical analysis , differential (mechanical device) , integral equation , nonlinear system , computer science , physics , first order partial differential equation , ecology , quantum mechanics , machine learning , artificial neural network , biology , thermodynamics
Stability properties of numerical methods for Volterra integro differential equations based on the convolution test equation\documentclass{article}\pagestyle{empty}\begin{document}$$ y\prime\left( t\right) = \gamma y\left( t \right) + \int\limits_0^t {\left( {\lambda + \mu \left( {t - s} \right)} \right)y\left( s \right)ds,} \,\,\,\,\,\,\,\,t \mathbin{\lower.3ex\hbox{$\buildrel>\over {\smash{\scriptstyle=}\vphantom{_x}}$}} 0,\,\,\,\,\,\,\,y\left( 0 \right) = 1, $$\end{document} are investigated. Stability regions of reducible linear multistep methods and modified multilag methods are given and compared.