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2021 A Pseudo-spectral Method for Time Distributed Order Two-sided Space Fractional Differential Equations
Shina Daniel Oloniiju, Sicelo Praisegod Goqo, Precious Sibanda
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Taiwanese J. Math. Advance Publication 1-21 (2021). DOI: 10.11650/tjm/210501

Abstract

Time distributed order two-sided space differential equations of arbitrary order offer a robust approach to modelling complex dynamical systems. In this study, we describe a scheme for obtaining the numerical solutions of time distributed order multidimensional two-sided space fractional differential equations. The numerical discretization scheme is a hybrid scheme, comprising a Newton–Cotes quadrature formula and a spectral collocation method. The time distributed order fractional differential operator is approximated using the composite Simpson's rule, and the solution of the resulting differential equation is expressed as a linear combination of shifted Chebyshev polynomials in all variables. Convergence analysis of the numerical scheme is presented. Some one- and two-dimensional time distributed order two-sided space fractional differential equations, such as the fractional advection-dispersion and diffusion equations, are presented to demonstrate the accuracy and computational efficiency of the numerical scheme, and numerical solutions are compared with the exact solutions, where these are available.

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Shina Daniel Oloniiju. Sicelo Praisegod Goqo. Precious Sibanda. "A Pseudo-spectral Method for Time Distributed Order Two-sided Space Fractional Differential Equations." Taiwanese J. Math. Advance Publication 1 - 21, 2021. https://doi.org/10.11650/tjm/210501

Information

Published: 2021
First available in Project Euclid: 24 May 2021

Digital Object Identifier: 10.11650/tjm/210501

Subjects:
Primary: 26A33, 65M70

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

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