Structure preserving computational technique for fractional order Schnakenberg model.

Iqbal, Zafar; Ahmed, Nauman; Baleanu, Dumitru; Rafiq, Muhammad; Iqbal, Muhammad Sajid; Rehman, Muhammad Aziz-ur

The current article deals with the analysis and numerical solution of fractional order Schnakenberg (S-B) model. This model is a system of autocatalytic reactions by nature, which arises in many biological systems. This study is aiming at investigating the behavior of natural phenomena with a more realistic and practical approach. The solutions are obtained by applying the Grunwald–Letnikov (G–L) finite difference (FD) and the proposed G–L nonstandard finite difference (NSFD) computational schemes. The proposed formulation is explicit in nature, strongly structure preserving as well as it is independent of the time step size. One very important feature of our proposed scheme is that it preserves the positivity of the solution of continuous fractional order S-B model because the unknown variables involved in this system describe the chemical concentrations of different substances. The comparison of the proposed scheme with G–L FD method reflects the significance of the said method.

FINITE differences; NUMERICAL solutions to differential equations; AUTOCATALYSIS; CHEMICAL systems; FRACTIONAL differential equations

Computational & Applied Mathematics, 2020, Vol 39, Issue 2, p1

0101-8205

Academic Journal

10.1007/s40314-020-1068-1