Discrete Hahn polynomials for numerical solution of two-dimensional variable-order fractional Rayleigh–Stokes problem

Journal Article · Sat Sep 15 04:00:00 EDT 2018 · Computational and Applied Mathematics

DOI:https://doi.org/10.1007/S40314-018-0631-5· OSTI ID:22769205

Salehi, Farideh ^[1]; Saeedi, Habibollah ^[2]

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1. Islamic Azad University, Department of Mathematics, Kerman Branch (Iran, Islamic Republic of)
2. Shahid Bahonar University of Kerman, Department of Applied Mathematics, Faculty of Mathematics and Computer (Iran, Islamic Republic of)

The main aim of this paper is to find the numerical solutions of 2D Rayleigh–Stokes problem with the variable-order fractional derivatives in the Riemann–Liouville sense. The presented method is based on collocation procedure in combination with the new operational matrix of the variable-order fractional derivatives, in the Caputo sense, for the discrete Hahn polynomials. The main advantage of the proposed method is obtaining a global approximation for spatial and temporal discretizations, and it reduced the problem to an algebraic system, which is easier to solve. Also, the profit of approximating a continuous function by Hahn polynomials is that for computing the coefficients of the expansion, we only have to compute a summation and the calculation of coefficients is exact. The error bound for the approximate solution is estimated. Finally, we evaluate results of the presented method with other numerical methods.

• OSTI ID: 22769205
• Journal Information: Computational and Applied Mathematics, Journal Name: Computational and Applied Mathematics Journal Issue: 4 Vol. 37; ISSN 0101-8205
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
APPROXIMATIONS
ERRORS
MATRICES
NUMERICAL SOLUTION
POLYNOMIALS
TWO-DIMENSIONAL CALCULATIONS