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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/668647
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