Application of homotopy analysis method to the solution of ninth order boundary value problems in AFTI-F16 fighters

Abstract

This paper is devoted to the study of ninth order boundary value problems that emerge in the mathematical modeling of AFTI-F16 fighter. An augmented longitudinal and lateral dynamics of the AFTI-F16 fighter is described by ninth order differential equations, containing unknown parameters which can be determined using automated system identification algorithms. The solution of the boundary value problem is obtained in terms of a convergent series using homotopy analysis method (HAM). The method is effectively applied on numerical examples and the results are compared with those given in the literature, revealing that the presented method gives better approximations to the exact solution.

Boundary-domain integral method and homotopy analysis method for systems of nonlinear boundary value problems in environmental engineering

“…Following that, the application of this method was widespread. It was successfully used to solve many linear and nonlinear equations and problems, for example: simulation of nonlinear water waves (Tao, Song, & Chakrabarti, 2007), nonlinear heat transfer (Abbasbandy, 2006;2007;Rashidi et al, 2014;Sajid & Hayat, 2008),differential-difference equation (Wang, Zou, & Zhang, 2007), solving cubic and coupled nonlinear Schr€ odinger equations (Hassan & El-Tawil, 2011) and many others (Akram & Sadaf, 2017;Alamri, Ellahi, Shehzad, & Zeeshan, 2019;Ellahi, 2013;Khan, Bukhari, Marin, & Ellahi, 2019;Kumar & Kumar, 2014;Prakash, Tripathi, Triwari, Sait, & Ellahi, 2019;Riaz, Ellahi, Bhatti, & Marin, 2019;Zeeshan, Shehzad, Abbas, & Ellahi, 2019). These successful applications affirmed the authenticity, flexibility and effectiveness of HAM.…”

“…The normalized system parameters are a 1 , a 2 , b 1 and b 2 : The carbon dioxide concentration at catalyst surface is denoted by k Finally, the dimensionless distance from the centre is x (Duan et al, 2015). Adomian (1994), Duan et al (2015), Biazar, Babolian, and Islam (2004), have used the Adomian decomposition method to develop a solution of this problem. They transform the governing equations into a system of coupled integral equations.…”

“…The original HAM has been upgraded by introducing an auxiliary parameter h, which enables control of the convergence of the series. With this modification, the HAM is more efficient than the ADM (Adomian, 1994).…”

A modified Fourier-Fick analysis for modeling non-Newtonian mixed convective flow considering heat generation

“…In addition, mixed convection, variable type conductivity/diffusivity and heat source characteristics are considered. Non-linear systems are tackled through homotopy algorithm [16][17][18][19][20][21][22][23][24][25]. The non-dimensional quantities are exhibited and deliberated.…”

Heat and Mass Transfer of Magnetohydrodynamics (MHD) Boundary Layer Flow using Homotopy Analysis Method

“…The homotopy analysis method was developed by Shijun Liao in 1992 that includes some unique concepts such as providing a great freedom to adjust and control the convergence region of solution series [20]. HAM able to provides an analytical approximation solution on numerous nonlinear problems such as nonlinear ordinary differential equations in boundary-layer flow problems, nonlinear fractional differential equations, homogeneous and nonhomogeneous nonlinear differential equations, and higher-order nonlinear differential equations as in [21][22][23][24][25].…”