Generalized Shifted Airfoil Polynomials of the Second Kind to Solve a Class of Singular Electrohydrodynamic Fluid Model of Fractional Order

Fractal and Fractional

article

Hari M. Srivastava¹  Mohammad Izadi⁵ 

[1] Department of Mathematics and Statistics, University of Victoria;Department of Medical Research, China Medical University Hospital, China Medical University;Department of Mathematics and Informatics, Azerbaijan University;Center for Converging Humanities, Kyung Hee University;Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman

关键词: collocation points;    convergent analysis;    electrohydrodynamic flow;    Liouville-Caputo fractional derivative;    shifted airfoil polynomials;    singular ODEs;    strongly nonlinearity;   

DOI  :  10.3390/fractalfract7010094

学科分类：社会科学、人文和艺术（综合）

来源: mdpi

【 摘 要 】

In this manuscript, we find the numerical solutions of a class of fractional-order differential equations with singularity and strong nonlinearity pertaining to electrohydrodynamic flow in a circular cylindrical conduit. The nonlinearity of the underlying model is removed by the quasilinearization method (QLM) and we obtain a family of linearized equations. By making use of the generalized shifted airfoil polynomials of the second kind (SAPSK) together with some appropriate collocation points as the roots of SAPSK, we arrive at an algebraic system of linear equations to be solved in an iterative manner. The error analysis and convergence properties of the SAPSK are established in the L 2 and L ∞ norms. Through numerical simulations, it is shown that the proposed hybrid QLM-SAPSK approach is not only capable of tackling the inherit singularity at the origin, but also produces effective numerical solutions to the model problem with different nonlinearity parameters and two fractional order derivatives. The accuracy of the present technique is checked via the technique of residual error functions. The QLM-SAPSK technique is simple and efficient for solving the underlying electrohydrodynamic flow model. The computational outcomes are accurate in comparison with those of numerical values reported in the literature.

【 授权许可】

CC BY