A new framework for polynomial approximation to differential equations

Abstract

In this paper we discuss a framework for the polynomial approximation to the solution of initial value problems for differential equations. The framework, initially devised for the approximation of ordinary differential equations, is further extended to cope with constant delay differential equations. Relevant classes of Runge-Kutta methods can be derived within this framework.

35 pages, 4 figures, 2 tables

References in corpus (2)

• The hidden side of COVID-19 spread in Italy
• A note on the continuous-stage Runge-Kutta-(Nyström) formulation of Hamiltonian Boundary Value Methods (HBVMs)

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• A spectrally accurate step-by-step method for the numerical solution of fractional differential equations
• Numerical solution of FDE-IVPs by using Fractional HBVMs: the fhbvm code
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• A shooting-Newton procedure for solving fractional terminal value problems