The aim of the present paper is to study the stability properties of the numerical methods for pure delay differential equations. The methods we consider are based on a quadrature rule and an interpolant (NCE) to get an approximation of the retarded part (continuous quadrature rule). As a test equation we consider y'(t) = -SUM_(r=1)^R b(r)(t)y(t - r tau), t > 0; y(t) = phi(t), t less-than-or-equal-to 0 and we give sufficient conditions for the boundedness of the solutions. The same behaviour is preserved by the continuous quadrature rule under some restriction on the parameters. As a conclusion we give some examples.
On the stability of continuous quadrature rules for differential equations with several constant delays
VERMIGLIO, Rossana
1993-01-01
Abstract
The aim of the present paper is to study the stability properties of the numerical methods for pure delay differential equations. The methods we consider are based on a quadrature rule and an interpolant (NCE) to get an approximation of the retarded part (continuous quadrature rule). As a test equation we consider y'(t) = -SUM_(r=1)^R b(r)(t)y(t - r tau), t > 0; y(t) = phi(t), t less-than-or-equal-to 0 and we give sufficient conditions for the boundedness of the solutions. The same behaviour is preserved by the continuous quadrature rule under some restriction on the parameters. As a conclusion we give some examples.File in questo prodotto:
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