Nowadays, fractional differential equations are a well established tool to model phenomena from the real world. Since the analytical solution is rarely available, there is a great effort in constructing efficient numerical methods for their solution. In this paper we are interested in solving boundary value problems having space derivative of fractional order. To this end, we present a collocation method in which the solution of the fractional problem is approximated by a spline quasi-interpolant operator. This allows us to construct the numerical solution in an easy way. We show through some numerical tests that the proposed method is efficient and accurate.

Quasi-interpolant operators and the solution of fractional differential problems / Pellegrino, E.; Pezza, L.; Pitolli, F.. - 336:(2021), pp. 207-218. (Intervento presentato al convegno International Conference on Approximation Theory XVI, 2019 tenutosi a USA) [10.1007/978-3-030-57464-2_11].

Quasi-interpolant operators and the solution of fractional differential problems

Pezza L.;Pitolli F.
2021

Abstract

Nowadays, fractional differential equations are a well established tool to model phenomena from the real world. Since the analytical solution is rarely available, there is a great effort in constructing efficient numerical methods for their solution. In this paper we are interested in solving boundary value problems having space derivative of fractional order. To this end, we present a collocation method in which the solution of the fractional problem is approximated by a spline quasi-interpolant operator. This allows us to construct the numerical solution in an easy way. We show through some numerical tests that the proposed method is efficient and accurate.
2021
International Conference on Approximation Theory XVI, 2019
B-spline; Collocation method; Fractional differential problem; Quasi-interpolant
04 Pubblicazione in atti di convegno::04b Atto di convegno in volume
Quasi-interpolant operators and the solution of fractional differential problems / Pellegrino, E.; Pezza, L.; Pitolli, F.. - 336:(2021), pp. 207-218. (Intervento presentato al convegno International Conference on Approximation Theory XVI, 2019 tenutosi a USA) [10.1007/978-3-030-57464-2_11].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1540687
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