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;
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.
File in questo prodotto:
File Dimensione Formato  
axioms-10-00249_Pellegrino.pdf

accesso aperto

Tipologia: Documento in Versione Editoriale
Licenza: Dominio pubblico
Dimensione 547.52 kB
Formato Adobe PDF
547.52 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/171551
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact