In this paper, we discuss a framework for the polynomial approximation to the sol tion of initial value problems for differential equations. The framework is based on an expansion of the vector field along an orthonormal basis, and relies on perturbation results for the considered problem. Initially devised for the approximation of ordinary differential equations, it is here further extended and, moreover, generalized to cope with constant delay differential equations. Relevant classes of Runge-Kutta methods can be derived within this framework.

A new framework for polynomial approximation to differential equations / Brugnano, Luigi; Frasca-Caccia, Gianluca; Iavernaro, Felice; Vespri, Vincenzo. - In: ADVANCES IN COMPUTATIONAL MATHEMATICS. - ISSN 1019-7168. - STAMPA. - 48:(2022), pp. 76.1-76.36. [10.1007/s10444-022-09992-w]

A new framework for polynomial approximation to differential equations

Brugnano, Luigi;Vespri, Vincenzo
2022

Abstract

In this paper, we discuss a framework for the polynomial approximation to the sol tion of initial value problems for differential equations. The framework is based on an expansion of the vector field along an orthonormal basis, and relies on perturbation results for the considered problem. Initially devised for the approximation of ordinary differential equations, it is here further extended and, moreover, generalized to cope with constant delay differential equations. Relevant classes of Runge-Kutta methods can be derived within this framework.
48
1
36
Brugnano, Luigi; Frasca-Caccia, Gianluca; Iavernaro, Felice; Vespri, Vincenzo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/1289818
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