Convergence analysis of a finite difference scheme for a two-point boundary value problem with a Riemann–Liouville–Caputo fractional derivative

Gracia, José Luis (Universidad de Zaragoza) ; O’Riordan, Eugene ; Stynes, Martin

Resumen: The Riemann–Liouville–Caputo (RLC) derivative is a new class of derivative that is motivated by modelling considerations; it lies between the more familiar Riemann–Liouville and Caputo derivatives. The present paper studies a two-point boundary value problem on the interval [0,  L] whose highest-order derivative is an RLC derivative of order a¿ (1 , 2). It is shown that the choice of boundary condition at x= 0 strongly influences the regularity of the solution. For the case where the solution lies in C1[0 , L] n Cq + 1(0 , L] for some positive integer q, a finite difference scheme is used to solve the problem numerically on a uniform mesh. In the error analysis of the scheme, the weakly singular behaviour of the solution at x= 0 is taken into account and it is shown that the method is almost first-order convergent. Numerical results are presented to illustrate the performance of the method.

Idioma: Inglés

DOI: 10.1007/s10543-019-00777-0

Año: 2020

Publicado en: BIT Numerical Mathematics 60, 2 (2020), 411-439
ISSN: 0006-3835

Factor impacto JCR: 1.663 (2020)

Categ. JCR: MATHEMATICS, APPLIED rank: 102 / 265 = 0.385 (2020) - Q2 - T2
Categ. JCR: COMPUTER SCIENCE, SOFTWARE ENGINEERING rank: 64 / 108 = 0.593 (2020) - Q3 - T2

Factor impacto SCIMAGO: 0.904 - Applied Mathematics (Q1) - Software (Q1) - Computer Networks and Communications (Q1) - Computational Mathematics (Q1)

Financiación: info:eu-repo/grantAgreement/ES/DGA-FSE/E24-17R
Financiación: info:eu-repo/grantAgreement/ES/MCYT-FEDER/MTM2016-75139-R
Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2016-75139-R

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)