A Fourth Order Non-Polynomial Quintic Spline Collocation Technique for Solving Time Fractional Superdiffusion Equations
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Date
2019
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Open Access Color
GOLD
Green Open Access
No
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Publicly Funded
No
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Top 10%
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Average
Popularity
Top 10%
Abstract
The purpose of this article is to present a technique for the numerical solution of Caputo time fractional superdiffusion equation. The central difference approximation is used to discretize the time derivative, while non-polynomial quintic spline is employed as an interpolating function in the spatial direction. The proposed method is shown to be unconditionally stable and O(h(4) + Delta t(2)) accurate. In order to check the feasibility of the proposed technique, some test examples have been considered and the simulation results are compared with those available in the existing literature.
Description
Abbas, Dr. Muhammad/0000-0002-0491-1528; Iqbal, Muhammad Kashif/0000-0003-4442-7498
Keywords
Non-Polynomial Quintic Spline, Finite Central Difference Approach, Superdiffusion Equation, Caputo Time Fractional Derivative, Numerical Analysis, Time-Fractional Diffusion Equation, Fractional Differential Equations, Non-polynomial quintic spline, Applied Mathematics, Finite central difference approach, Theory and Applications of Fractional Differential Equations, Computer science, Superdiffusion equation, Algorithm, Semilinear Differential Equations, Caputo time fractional derivative, Numerical Methods for Singularly Perturbed Problems, Modeling and Simulation, Physical Sciences, QA1-939, FOS: Mathematics, Fractional Calculus, Anomalous Diffusion Modeling and Analysis, Mathematics, Fractional derivatives and integrals, finite central difference approach, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Caputo fractional derivative, non-polynomial quintic spline, Fractional partial differential equations, superdiffusion equation, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
Fields of Science
01 natural sciences, 0103 physical sciences
Citation
Amin, Muhammad...et al. (2019) "A Fourth Order Non-Polynomial Quintic Spline Collocation Technique for Solving Time Fractional Superdiffusion Equations", Advances in Difference Equations, Vol. 2019, No. 1.
WoS Q
Q1
Scopus Q
OpenCitations Citation Count
15
Source
Advances in Difference Equations
Volume
2019
Issue
1
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End Page
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CrossRef : 3
Scopus : 22
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Mendeley Readers : 9
SCOPUS™ Citations
22
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Web of Science™ Citations
18
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4
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