A GEOMETRICALLY CONVERGENT PSEUDO–SPECTRAL METHOD FOR MULTI–DIMENSIONAL TWO–SIDED SPACE FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

Shina D. Oloniiju; Sicelo P. Goqo; Precious Sibanda

doi:10.11948/20200023

2021 Volume 11 Issue 4

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Shina D. Oloniiju, Sicelo P. Goqo, Precious Sibanda. A GEOMETRICALLY CONVERGENT PSEUDO–SPECTRAL METHOD FOR MULTI–DIMENSIONAL TWO–SIDED SPACE FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 1699-1717. doi: 10.11948/20200023

Citation:

Shina D. Oloniiju, Sicelo P. Goqo, Precious Sibanda. A GEOMETRICALLY CONVERGENT PSEUDO–SPECTRAL METHOD FOR MULTI–DIMENSIONAL TWO–SIDED SPACE FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 1699-1717. doi: 10.11948/20200023

A GEOMETRICALLY CONVERGENT PSEUDO–SPECTRAL METHOD FOR MULTI–DIMENSIONAL TWO–SIDED SPACE FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

1.
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg, 3209, South Africa

Corresponding author: Email: shina@aims.edu.gh(S. D. Oloniiju)

Abstract

Abstract

In this study, we present a geometrically convergent numerical method for solving multi-dimensional two-sided space-time fractional differential equations. The approach represents the solutions of the differential equations in terms of the shifted Chebyshev polynomials. The expansions are evaluated at the shifted Chebyshev-Gauss-Lobatto nodes. We present the approximations for left-sided integration, and the left- and right- sided differentiation. The performance of the method is demonstrated using some two-sided space fractional partial differential equations in one and two dimensions. The numerical results obtained show that the method is accurate and computationally efficient. A theoretical analysis of the convergence of the method is presented, where it is shown that, given a continuously differentiable solution, the numerical solution converges for a sufficiently large number of grid points.
- Shifted Chebyshev polynomials /
- Chebyshev-Gauss-Lobatto quadrature /
- two-sided space-time fractional partial differentials /
- fractional calculus /
- convergence analysis
MSC: 26A33, 65M70

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References

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