Nonlinear fractional differential equations are widely used to model real-life phenomena. For this reason, there is a need for efficient numerical methods to solve such problems. In this respect, collocation methods are particularly attractive for their ability to deal with the nonlocal behavior of the fractional derivative. Among the variety of collocation methods, methods based on spline approximations are preferable since the approximations can be represented by local bases, thereby reducing the computational load. In this paper, we use a collocation method based on spline quasi-interpolant operators to solve nonlinear time-fractional initial value problems. The numerical tests we performed show that the method has good approximation properties.

Applications of optimal spline approximations for the solution of nonlinear time-fractional initial value problems / Pellegrino, Enza; Pitolli, Francesca. - In: AXIOMS. - ISSN 2075-1680. - 10:4(2021), p. 249. [10.3390/axioms10040249]

Applications of optimal spline approximations for the solution of nonlinear time-fractional initial value problems

Pitolli, Francesca
2021

Abstract

Nonlinear fractional differential equations are widely used to model real-life phenomena. For this reason, there is a need for efficient numerical methods to solve such problems. In this respect, collocation methods are particularly attractive for their ability to deal with the nonlocal behavior of the fractional derivative. Among the variety of collocation methods, methods based on spline approximations are preferable since the approximations can be represented by local bases, thereby reducing the computational load. In this paper, we use a collocation method based on spline quasi-interpolant operators to solve nonlinear time-fractional initial value problems. The numerical tests we performed show that the method has good approximation properties.
2021
fractional differential equation; quasi-interpolant operator; collocationmethod; optimal spline
01 Pubblicazione su rivista::01a Articolo in rivista
Applications of optimal spline approximations for the solution of nonlinear time-fractional initial value problems / Pellegrino, Enza; Pitolli, Francesca. - In: AXIOMS. - ISSN 2075-1680. - 10:4(2021), p. 249. [10.3390/axioms10040249]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1580254
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