Numerical methods of the variable-order Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative

Chen, C.M., Liu, F., Burrage, K., & Chen, Y. (2012) Numerical methods of the variable-order Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative. IMA Journal of Applied Mathematics, pp. 1-21.

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Abstract

Rayleigh–Stokes problems have in recent years received much attention due to their importance in physics. In this article, we focus on the variable-order Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivative. Implicit and explicit numerical methods are developed to solve the problem. The convergence, stability of the numerical methods and solvability of the implicit numerical method are discussed via Fourier analysis. Moreover, a numerical example is given and the results support the effectiveness of the theoretical analysis.

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65 since deposited on 15 May 2013
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ID Code: 60015
Item Type: Journal Article
Refereed: Yes
Keywords: variable-order fractional derivative, Rayleigh–Stokes problem, implicit numerical method, explicit numerical method, convergence, stability, solvability, Fourier analysis
DOI: 10.1093/imamat/hxr079
ISSN: 1464-3634(online) 0272-4960 (print)
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Analysis (010301)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2012 The Author. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Deposited On: 15 May 2013 22:47
Last Modified: 17 May 2013 17:39

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