Show simple item record

dc.contributor.advisorYan, Yubinen
dc.contributor.authorBroadbent, Emma*
dc.date.accessioned2018-03-26T14:46:21Z
dc.date.available2018-03-26T14:46:21Z
dc.date.issued2017-10
dc.identifier.citationBroadbent, E. (2017). Numerical Methods for Solving Nonlinear Fractional Differential Equations with Non-Uniform Meshes. (Masters thesis). University of Chester, United Kingdom.en
dc.identifier.urihttp://hdl.handle.net/10034/621033
dc.description.abstractIn this dissertation, we consider numerical methods for solving fractional differential equations with non-uniform meshes. We first introduce some basic definitions and theories for fractional differential equations and then we consider the numerical methods fro solving fractional differential equation. In the literature, the popular numerical methods for solving fractional differential equation include the rectangle method, trapezoid method and predictor-corrector methods. We reviewed such methods and the ways to prove the stability and the error estimates for these methods. Since the fractional differential equation is a nonlocal problem, the computation cost is very long compared with the local problem. Therefore it is very important to design some higher order numerical methods for solving fractional differential equation. In this dissertation, we introduce a new higher order numerical method for solving fractional differential equation which is based on the quadratic interpolation polynomial approximation to the fractional integral. To capture the singularity near the origin we also introduce the non-uniform meshes. The numerical results show that the optimal convergence order can be recovered by using non-uniform meshes even if the data are not sufficiently smooth.
dc.language.isoenen
dc.publisherUniversity of Chesteren
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectfractional differential equationsen
dc.subjectCaputo derivativeen
dc.subjectnon-uniform meshesen
dc.titleNumerical Methods for Solving Nonlinear Fractional Differential Equations with Non-Uniform Meshesen
dc.typeThesis or dissertationen
dc.type.qualificationnameMScen
dc.type.qualificationlevelMasters Degreeen
html.description.abstractIn this dissertation, we consider numerical methods for solving fractional differential equations with non-uniform meshes. We first introduce some basic definitions and theories for fractional differential equations and then we consider the numerical methods fro solving fractional differential equation. In the literature, the popular numerical methods for solving fractional differential equation include the rectangle method, trapezoid method and predictor-corrector methods. We reviewed such methods and the ways to prove the stability and the error estimates for these methods. Since the fractional differential equation is a nonlocal problem, the computation cost is very long compared with the local problem. Therefore it is very important to design some higher order numerical methods for solving fractional differential equation. In this dissertation, we introduce a new higher order numerical method for solving fractional differential equation which is based on the quadratic interpolation polynomial approximation to the fractional integral. To capture the singularity near the origin we also introduce the non-uniform meshes. The numerical results show that the optimal convergence order can be recovered by using non-uniform meshes even if the data are not sufficiently smooth.


Files in this item

Thumbnail
Name:
1_Emma Broadbent.pdf
Size:
670.8Kb
Format:
PDF
Request:
Main thesis

This item appears in the following Collection(s)

Show simple item record

http://creativecommons.org/licenses/by-nc-nd/4.0/
Except where otherwise noted, this item's license is described as http://creativecommons.org/licenses/by-nc-nd/4.0/