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 inNumerical algorithms Vol. 74; no. 3; pp. 717 - 754
Main Authors Deng, Jingwei, Zhao, Lijing, Wu, Yujiang
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2017
Springer Nature B.V
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
Equidistributing meshes
Fast predictor-corrector approach
Tempered fractional ordinary differential equation
65L12
Short memory principle
34A08
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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