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dc.contributor.authorFan, Lili*
dc.contributor.authorYan, Yubin*
dc.date.accessioned2019-03-04T11:29:00Z
dc.date.available2019-03-04T11:29:00Z
dc.date.issued2019-01-18
dc.identifier.citationFan, L., & Yan Y. (2019). A high order numerical method for solving nonlinear fractional differential equation with non-uniform meshes. In G. Nikolov, N. Kolkovska, & K. Georgiev (Eds.) Numerical methods and applications: 9th International Conference, Borovets, Bulgaria, August 20-24, 2018. Springer.en
dc.identifier.isbn9783030106911
dc.identifier.doi10.1007/978-3-030-10692-8_23
dc.identifier.urihttp://hdl.handle.net/10034/621938
dc.description.abstractWe introduce a high-order numerical method for solving nonlinear fractional differential equation with non-uniform meshes. We first transform the fractional nonlinear differential equation into the equivalent Volterra integral equation. Then we approximate the integral by using the quadratic interpolation polynomials. On the first subinterval $[t_{0}, t_{1}]$, we approximate the integral with the quadratic interpolation polynomials defined on the nodes $t_{0}, t_{1}, t_{2}$ and in the other subinterval $[t_{j}, t_{j+1}], j=1, 2, \dots N-1$, we approximate the integral with the quadratic interpolation polynomials defined on the nodes $t_{j-1}, t_{j}, t_{j+1}$. A high-order numerical method is obtained. Then we apply this numerical method with the non-uniform meshes with the step size $\tau_{j}= t_{j+1}- t_{j}= (j+1) \mu$ where $\mu= \frac{2T}{N (N+1)}$. Numerical results show that this method with the non-uniform meshes has the higher convergence order than the standard numerical methods obtained by using the rectangle and the trapzoid rules with the same non-uniform meshes.
dc.language.isoenen
dc.publisherSpringeren
dc.relation.ispartofseriesLecture Notes in Computer Science, volume 11189
dc.relation.urlhttps://link.springer.com/chapter/10.1007/978-3-030-10692-8_23en
dc.relation.urlhttps://link.springer.com/book/10.1007/978-3-030-10692-8
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.subjectnumerical methodsen
dc.subjectnonuniform meshesen
dc.subjectfractional derivativeen
dc.titleA high order numerical method for solving nonlinear fractional differential equation with non-uniform meshesen
dc.typeBook chapteren
dc.contributor.departmentUniversity of Chester; Lvliang Universityen
dc.date.accepted2019-01-10
or.grant.openaccessYesen
rioxxterms.funderunfundeden_US
rioxxterms.identifier.projectunfundeden_US
rioxxterms.versionAMen
rioxxterms.licenseref.startdate2020-01-18
rioxxterms.publicationdate2019-01-18


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