Short memory principle and a predictor-corrector approach for fractional differential equations

By Weihua Deng. 2007

278 citations recorded by the source corpus.

Fractional differential equations are increasingly used to model problems in acoustics and thermal systems, rheology and modelling of materials and mechanical systems, signal processing and systems identification, control and robotics, and other areas of application. This paper further analyses the underlying structure of fractional differential equations. From a new point of view, we apprehend the short memory principle of fractional calculus and farther apply a Adams-type predictor-corrector approach for the numerical solution of fractional differential equation. And the detailed error analysis is presented. Combining the short memory principle and the predictor-corrector approach, we gain a good numerical approximation of the true solution of fractional differential equation at reasonable computational cost. A numerical example is provided and compared with the exact analytical solution for illustrating the effectiveness of the short memory principle.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/173b9536d8ed1ca481c3d70d9540c395fd03894b

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Citations in the corpus

A new formula for fractional integrals of Chebyshev polynomials: Application for solving multi-term fractional differential equations (2013, methodology): “Numerical results of this FDE show that the SCT method is more accurate than the short memory principle and a predictor–corrector approach introduced by Deng [34], see Table 1 in [34].”
Application of measure of noncompactness to a Cauchy problem for fractional differential equations in Banach spaces (2013, background): “To see more about applications, we also refer the reader to ([17], [21]-[25]).”
Variational iteration method for the Burgers' flow with fractional derivatives—New Lagrange multipliers (2013, unknown): “Some numerical methods [1–6] and analytical methods [7–12] have been developed for fractional differential equations (FDEs).”
A pseudo-spectral scheme for the approximate solution of a family of fractional differential equations (2011, methodology): “t Our method Method of [33] Method of [15] n = 10 n = 15 n = 20 h 1⁄4 1 20 h 1⁄4 1 320 p = 1, T = 1 p = 4, T = 2 1 6.”
Higher order numerical methods for solving fractional differential equations (2014, unknown): “, [3–5, 12, 14], etc.”
Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial (2018, background): “, see [39]) or on some more sophisticated approaches [40,41], their use introduces a further source of errors and/or increases the computational complexity.”