A Pseudo-spectral Method for Time Distributed Order Two-sided Space Fractional Differential Equations

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 differentia...

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Published in:Taiwanese journal of mathematics 2021-10, Vol.25 (5), p.959-979
Main Authors: Oloniiju, Shina Daniel, Goqo, Sicelo Praisegod, Sibanda, Precious
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Language:English
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description 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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title A Pseudo-spectral Method for Time Distributed Order Two-sided Space Fractional Differential Equations
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