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

Abstract

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 L2 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.

Hybrid technique of conformal mapping and Chebyshev collocation method for solving time–space fractional order wave equation

“…Every day, substantial efforts are undertaken to solve differential equations, which have numerous applications in various scientific domains 1–3 . Fractional‐order differential equations (FDEs) have been successfully used to describe phenomena in various scientific and engineering fields, including fluid mechanics, medicine, heat conduction, electromagnetism, viscoelasticity, biology, wave propagation, optimal control, and more 4–14 . As a result of their importance, solutions to fractional ordinary or partial differential equations with physical meaning have received special attention.…”

“…[1][2][3] Fractional-order differential equations (FDEs) have been successfully used to describe phenomena in various scientific and engineering fields, including fluid mechanics, medicine, heat conduction, electromagnetism, viscoelasticity, biology, wave propagation, optimal control, and more. [4][5][6][7][8][9][10][11][12][13][14] As a result of their importance, solutions to fractional ordinary or partial differential equations with physical meaning have received special attention. As a result, mathematicians and researchers focus heavily on developing analytical solutions to fractional partial differential equations (FPDEs) of this type.…”

A novel Touchard polynomial-based spectral matrix collocation method for solving the Lotka-Volterra competition system with diffusion

“…The applications of the spectral collocation approach with exponential-order accuracy have been examined for various model problems in physical sciences. For example, we may draw your attention to the recently published works [23][24][25][26][27][28][29][30]. The Touchard polynomials, also known as Touchard-Riordan polynomials or exponential polynomials, constitute a family of functions prominent in combinatorics and partition theory [31].…”