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Numerical approximation of the nonlinear time-fractional telegraph equation arising in neutron transport
| dc.contributor.author | Nikan, O. | |
| dc.contributor.author | Avazzadeh, Z. | |
| dc.contributor.author | Tenreiro Machado, J. A. | |
| dc.date.accessioned | 2021-07-06T14:16:12Z | |
| dc.date.embargo | 2100 | |
| dc.date.issued | 2021 | |
| dc.description.abstract | This paper focusses on the numerical solution of the nonlinear time-fractional telegraph equation formulated in the Caputo sense. This model is a useful description of the neutron transport process inside the core of a nuclear reactor. The proposed method approximates the unknown solution with the help of two main stages. At a first stage, a semi-discrete algorithm is obtained by means of a difference approach with the accuracy O(τ3−β), where 1<β<2 is the fractional-order derivative. At a second stage, a full-discretization is obtained by an efficient augmented local radial basis function finite difference (LRBF-FD). This method approximates the derivatives of an unknown function at a given point named as center, based on the finite difference at each local-support domain, instead of applying the entire set of points. The technique produces a sparse matrix system, reduces the computational effort and avoids the ill-conditioning derived from the global collocation. The unconditional stability and convergence of the time-discretized formulation are demonstrated and confirmed numerically. The numerical results highlight the accuracy and the validity of the method. | pt_PT |
| dc.description.version | info:eu-repo/semantics/publishedVersion | pt_PT |
| dc.identifier.doi | 10.1016/j.cnsns.2021.105755 | pt_PT |
| dc.identifier.issn | 1007-5704 | |
| dc.identifier.uri | http://hdl.handle.net/10400.22/18095 | |
| dc.language.iso | eng | pt_PT |
| dc.publisher | Elsevier | pt_PT |
| dc.relation.publisherversion | https://www.sciencedirect.com/science/article/pii/S1007570421000666#! | pt_PT |
| dc.subject | Fractional telegraph equation | pt_PT |
| dc.subject | Caputo fractional derivative | pt_PT |
| dc.subject | RBF | pt_PT |
| dc.subject | LRBF-FD | pt_PT |
| dc.subject | Convergence | pt_PT |
| dc.subject | Stability | pt_PT |
| dc.title | Numerical approximation of the nonlinear time-fractional telegraph equation arising in neutron transport | pt_PT |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.startPage | 105755 | pt_PT |
| oaire.citation.title | Communications in Nonlinear Science and Numerical Simulation | pt_PT |
| oaire.citation.volume | 99 | pt_PT |
| person.familyName | Tenreiro Machado | |
| person.givenName | J. A. | |
| person.identifier.ciencia-id | 7A18-4935-5B29 | |
| person.identifier.orcid | 0000-0003-4274-4879 | |
| person.identifier.rid | M-2173-2013 | |
| person.identifier.scopus-author-id | 55989030100 | |
| rcaap.rights | closedAccess | pt_PT |
| rcaap.type | article | pt_PT |
| relation.isAuthorOfPublication | 82cd5c17-07b6-492b-b3e3-ecebdad1254f | |
| relation.isAuthorOfPublication.latestForDiscovery | 82cd5c17-07b6-492b-b3e3-ecebdad1254f |
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