We introduce a family of diagonally-implicit continuous methods for the numerical integration of Volterra Integral Equations. The derived methods are characterized by a lower triangular or diagonal coefficient matrix of the nonlinear system for the computation of the stages which, as it is known, can be exploited to get an efficient implementation. The constructed methods have a high uniform order of convergence together with strong stability properties (e.g. A-stability).

Two-step diagonally-implicit collocation-based methods for Volterra Integral Equations.

CONTE, Dajana;D'AMBROSIO, RAFFAELE;PATERNOSTER, Beatrice
2012-01-01

Abstract

We introduce a family of diagonally-implicit continuous methods for the numerical integration of Volterra Integral Equations. The derived methods are characterized by a lower triangular or diagonal coefficient matrix of the nonlinear system for the computation of the stages which, as it is known, can be exploited to get an efficient implementation. The constructed methods have a high uniform order of convergence together with strong stability properties (e.g. A-stability).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/2600430
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