Fast predictor-corrector approach for the tempered fractional differential equations

The tempered evolution equation describes the trapped dynamics, widely appearing in nature, e.g., the motion of living particles in viscous liquid. This paper proposes the fast predictor-corrector approach for the tempered fractional ordinary differential equations by digging out the potential ‘very...

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Bibliographic Details
Published in:Numerical algorithms 2017-03, Vol.74 (3), p.717-754
Main Authors: Deng, Jingwei, Zhao, Lijing, Wu, Yujiang
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Applied mathematics
Approximation
Calculus
Computer Science
Differential equations
Fractional calculus
Mathematical analysis
Numeric Computing
Numerical Analysis
Ordinary differential equations
Original Paper
Predictor-corrector methods
Theory of Computation
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Summary:The tempered evolution equation describes the trapped dynamics, widely appearing in nature, e.g., the motion of living particles in viscous liquid. This paper proposes the fast predictor-corrector approach for the tempered fractional ordinary differential equations by digging out the potential ‘very’ short memory principle. Algorithms based on the idea of equidistributing are detailedly described. Error estimates for the proposed schemes are derived; and the effectiveness and low computation cost, being linearly increasing with time t , are numerically demonstrated.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-016-0169-9