A second-order efficient L-stable numerical method for space fractional reaction–diffusion equations

ABSTRACT

In this article we are proposing a strongly stable computationally efficient method in time to numerically solve reaction–diffusion equations with space fractional derivative. The Riesz space fractional derivative is discretized using the second-order fractional centred difference method. Time stepping scheme is based on second-order exponential time differencing Runge–Kutta method. Second-order positivity preserving Padé approximations is used to develop the proposed L-stable method. The computation efficiency of the method is significantly enhanced by using partial fractions splitting technique. The method is shown to be stable and reliable. Solution profiles as well as convergence tables in time are presented for various values of diffusion rates α.

KEYWORDS:

• Space-fractional Allen–Cahn
• fractional enzyme kinetic
• Riesz fractional derivative
• exponential time differencing
• Padé approximation
• L-stable

2010 AMS SUBJECT CLASSIFICATIONS:

• 35R11
• 65N12
• 65N06
• 35B30
• 35B65

Acknowledgments

The authors would like to acknowledge the support provided by the Deanship of Scientific Research at King Fahd University of Petroleum & Minerals.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

M. Yousuf http://orcid.org/0000-0003-3893-4776