A finite difference method for an initial–boundary value problem with a Riemann–Liouville–Caputo spatial fractional derivative

Gracia, José Luis (Universidad de Zaragoza) ; Stynes, Martin

Resumen: An initial–boundary value problem with a Riemann–Liouville–Caputo space fractional derivative of order a¿(1, 2) is considered, where the boundary conditions are reflecting. A fractional Friedrichs’ inequality is derived and is used to prove that the problem approaches a steady-state solution when the source term is zero. The solution of the general problem is approximated using a finite difference scheme defined on a uniform mesh and the error analysis is given in detail for typical solutions which have a weak singularity near the spatial boundary x=0. It is proved that the scheme converges with first order in the maximum norm. Numerical results are given that corroborate our theoretical results for the order of convergence of the difference scheme, the approach of the solution to steady state, and mass conservation.

Idioma: Inglés

DOI: 10.1016/j.cam.2020.113020

Año: 2021

Publicado en: Journal of Computational and Applied Mathematics 381 (2021), 113020 1-14
ISSN: 0377-0427

Factor impacto JCR: 2.872 (2021)

Categ. JCR: MATHEMATICS, APPLIED rank: 37 / 267 = 0.139 (2021) - Q1 - T1

Factor impacto CITESCORE: 5.1 - Mathematics (Q1)

Factor impacto SCIMAGO: 0.875 - Computational Mathematics (Q2) - Applied Mathematics (Q2)

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

Tipo y forma: Article (PostPrint)

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