We propose a family of multivalue collocation methods for the numerical solution of differential problems, potentially candidate to be stiff. For this reason, the suggested numerical schemes have strong stability properties, such as A-stability. Moreover, in order to obtain an efficient implementation, it is desirable to impose the conditions gaining a structured coefficient matrix of the nonlinear system for the computation of the internal stages. The construction of these methods has been presented and the properties of the resulting formulae have been verified experimentally.

Semi-implicit Multivalue Almost Collocation Methods

D'Ambrosio R.;
2022

Abstract

We propose a family of multivalue collocation methods for the numerical solution of differential problems, potentially candidate to be stiff. For this reason, the suggested numerical schemes have strong stability properties, such as A-stability. Moreover, in order to obtain an efficient implementation, it is desirable to impose the conditions gaining a structured coefficient matrix of the nonlinear system for the computation of the internal stages. The construction of these methods has been presented and the properties of the resulting formulae have been verified experimentally.
978-0-7354-4182-8
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/186873
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