Numerical approach for solving space fractional orderdiffusion equations using shifted Chebyshev polynomials of the fourth kind

Authors

NASSER HASSAN SWIELAM
ABD ELHAMEED MOHAMED NAGY
ADEL ABD ELAZIZ EL SAYED

DOI

10.3906/mat-1503-20

Abstract

In this paper, a new approach for solving space fractional order diffusion equations is proposed. The fractional derivative in this problem is in the Caputo sense. This approach is based on shifted Chebyshev polynomials of the fourth kind with the collocation method. The finite difference method is used to reduce the equations obtained by our approach for a system of algebraic equations that can be efficiently solved. Numerical results obtained with our approach are presented and compared with the results obtained by other numerical methods. The numerical results show the efficiency of the proposed approach.

Keywords

Space fractional order diffusion equation, Caputo derivative, Chebyshev collocation method, finite difference method, Chebyshev polynomials of the fourth kind; Euler approximation

First Page

1283

Last Page

1297

Recommended Citation

SWIELAM, NASSER HASSAN; NAGY, ABD ELHAMEED MOHAMED; and SAYED, ADEL ABD ELAZIZ EL (2016) "Numerical approach for solving space fractional orderdiffusion equations using shifted Chebyshev polynomials of the fourth kind," Turkish Journal of Mathematics: Vol. 40: No. 6, Article 10. https://doi.org/10.3906/mat-1503-20
Available at: https://journals.tubitak.gov.tr/math/vol40/iss6/10