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NUMERICAL INVESTIGATION AND APPLICATION OF FRACTIONAL DYNAMICAL SYSTEMS

Part of: Real functions Partial differential equations, boundary value problems

Published online by Cambridge University Press:  23 October 2019

LIBO FENG Open the ORCID record for LIBO FENG [Opens in a new window]
LIBO FENG*
Affiliation:
School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Queensland 4001, Australia email fenglibo2012@126.com
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Abstract

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Keywords

fractional diffusion equationfinite element methodcontrol volume methodirregular convex domainunstructured meshfluid modelsstability and convergence analysis

MSC classification

Primary: 26A33: Fractional derivatives and integrals
Secondary: 65N06: Finite difference methods 65N08: Finite volume methods 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65N12: Stability and convergence of numerical methods
Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 1 , February 2020 , pp. 163 - 165
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

Footnotes

Thesis submitted to Queensland University of Technology in October 2018; degree approved on 28 February 2019; supervisors Fawang Liu, Ian Turner and Qianqian Yang.

References

Feng, L., Liu, F. and Turner, I., ‘Finite difference/finite element method for a novel 2D multi-term time-fractional mixed sub-diffusion and diffusion-wave equation on convex domains’, Commun. Nonlinear Sci. Numer. Simul. 70 (2019), 354–371.Google Scholar
Feng, L., Liu, F. and Turner, I., ‘An unstructured mesh control volume method for two-dimensional space fractional diffusion equations with variable coefficients on convex domains’, J. Comput. Appl. Math. 364 (2020), 112319.Google Scholar
Feng, L., Liu, F., Turner, I., Yang, Q. and Zhuang, P., ‘Unstructured mesh finite difference/finite element method for the 2D time-space Riesz fractional diffusion equation on irregular convex domains’, Appl. Math. Model. 59 (2018), 441–463.Google Scholar
Feng, L., Liu, F., Turner, I. and Zhuang, P., ‘Numerical methods and analysis for simulating the flow of a generalized Oldroyd-B fluid between two infinite parallel rigid plates’, Intl J. Heat Mass Transfer 115 (2017), 1309–1320.Google Scholar
Feng, L., Liu, F., Turner, I. and Zhuang, P., ‘Novel numerical analysis of multi-term time fractional viscoelastic non-Newtonian fluid models for simulating unsteady MHD Couette flow of a generalized Oldroyd-B fluid’, Fract. Calc. Appl. Anal. 21(4) (2018), 1073–1103.Google Scholar
Feng, L., Zhuang, P., Liu, F., Turner, I., Anh, V. and Li, J., ‘A fast second-order accurate method for a two-sided space-fractional diffusion equation with variable coefficients’, Comput. Math. Appl. 73 (2017), 1155–1171.Google Scholar
Li, J., Liu, F., Feng, L. and Turner, I., ‘A novel finite volume method for the Riesz space distributed-order diffusion equation’, Comput. Math. Appl. 74 (2017), 772–783.Google Scholar
Li, J., Liu, F., Feng, L. and Turner, I., ‘A novel finite volume method for the Riesz space distributed-order advection-diffusion equation’, Appl. Math. Model. 46 (2017), 536–553.Google Scholar