Stability and convergence of a numerical scheme for advection-diffusion equations involving a fractional Laplace operator
Martin Nitiema1, Somdouda Sawadogo2,
1 Université Joseph KI-ZERBO, Ouagadougou, Burkina Faso, and Laboratoire LAMIA, Université des Antilles, Pointe-à-Pitre, Guadeloupe
2 Ecole Normale Supérieure, Laboratoire LANIBIO, Ouagadougou, Burkina Faso
Received on November 28, 2022, revised version on January 16, 2023
Accepted on January 18, 2023
Communicated by Mahamadi Warma
| Abstract. We consider an advection-diffusion equation involving a Laplace fractional operator of order 1/2 < s < 1. We first assume that the solution of this equation is regular. Then we use a combination of left and right fractional Riemann-Liouville derivatives of order 2s to approximate the fractional Laplace operator. This allows us to obtain a numerical scheme of Euler explicit type which is proven to be conditionally stable, first order in time an space accurate. Numerical results are given to illustrate the results. | |
| Keywords: | C0 fractional Laplace operator, fractional Riemann-Liouville derivatives, Euler explicit scheme, stability and convergence. |
| 2010 Mathematics Subject Classification: 35R11; 35S15; 65M12. | |