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Applied Mathematics and Nonlinear Sciences
Volume 3 (2018): Issue 2 (July 2018)
Open Access
Review of numerical methods for NumILPT with computational accuracy assessment for fractional calculus
Dariusz W. Brzeziński
Dariusz W. Brzeziński
| Dec 01, 2018
Applied Mathematics and Nonlinear Sciences
Volume 3 (2018): Issue 2 (July 2018)
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Published Online:
Dec 01, 2018
Page range:
487 - 502
Received:
Aug 26, 2018
Accepted:
Nov 26, 2018
DOI:
https://doi.org/10.2478/AMNS.2018.2.00038
Keywords
Numerical Approximation of the Inverse Laplace Transform
,
Fractional order differential Equations
,
Multi-precision Computing
© 2018 Dariusz W. Brzeziński, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.
Fig. 1
Plots of numerical inversions f̂(t) of the Laplace transform (1) (a) and their relative errors (b) for applied methods in interval (0,10〉.
Fig. 2
Plots of numerical inversions f̂(t) of the Laplace transform (2) (a) and their relative errors (b) for applied methods in interval (0,30〉.
Fig. 3
Plots of numerical inversions f̂(t) of the Laplace transform (3) (a) and their relative errors (b) for applied methods in interval (0,30〉.
Fig. 4
Plots of numerical inversions f̂(t) of the Laplace transform (4) (a) and their relative errors (b) for applied methods in interval (0,50〉.
Fig. 5
Plots of numerical inversions f̂(t) of the Laplace transform (5) (a) and their relative errors (b) for applied methods in interval (0,30〉.
Fig. 6
Plots of numerical inversions f̂(t) of the Laplace transform (6) (a) and their relative errors (b) for applied methods in interval (0,30〉.
Fig. 7
Plots of numerical inversions f̂(t) of the Laplace transform (7) (a) and their relative errors (b) for applied methods in interval (0,30〉.
Fig. 8
Plots of numerical inversions f̂(t) of the Laplace transform (8) (a) and their relative errors (b) for applied methods in interval (0,30〉.
Fig. 9
Plots of numerical inversions f̂(t) of the Laplace transform (9) (a) and their relative errors (b) for applied methods in interval (0,30〉.
Fig. 10
Plots of numerical inversions f̂(t) of the Laplace transform (10) (a) and their relative errors (b) for applied methods in interval (0,20〉.