The first part of this paper studies the stability and the order of a numerical method for the integration of the second kind of Volterra equations. This method is obtained by differentiatingm-times (m>-2) the Volterra equation and by integrating the «differential equations system» obtained via the trapezoidal rule. The proposed method has second order and an absolute stability region equal to the third quadrant of the plane (hλ,h 2μ). The second part of this paper, analyzes the stability properties and also the order of a class of numerical methods, obtained via the integration of the previous «differential equations system» though backward differentiation. It is shown that these methods have a high order and a very large stability region.

Metodi numerici per equazioni di volterra di seconda specie

Giuseppe Piazza
1984-01-01

Abstract

The first part of this paper studies the stability and the order of a numerical method for the integration of the second kind of Volterra equations. This method is obtained by differentiatingm-times (m>-2) the Volterra equation and by integrating the «differential equations system» obtained via the trapezoidal rule. The proposed method has second order and an absolute stability region equal to the third quadrant of the plane (hλ,h 2μ). The second part of this paper, analyzes the stability properties and also the order of a class of numerical methods, obtained via the integration of the previous «differential equations system» though backward differentiation. It is shown that these methods have a high order and a very large stability region.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/7737
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