Construction of analytic solution to chaotic dynamical systems using the Homotopy analysis method

Travelling wave solutions: A new approach to the analysis of nonlinear physical phenomena

“…There are many papers that deal with HAM. Abbasbandy et al [13] applied the Newton-homotopy analysis method to solve nonlinear algebraic equations, Allan [14] constructed the analytical solutions to Lorenz system by the HAM, Bataineh et al [15,16] proposed a new reliable modification of the HAM, M. Ganjiani et al [17] constructed the analytical solutions to coupled nonlinear diffusion reaction equations by the HAM, Alomari et al [18] applied the HAM to study delay differential equations, Chen and Liu. [19] applied the HAM to increase the convergent region of the harmonic balance method.…”

Variational Iteration Method for Solving Differential Equations with Piecewise Constant Arguments

“…More materials of the classical solution techniques that are most commonly used to solve equations and systems, such as the Adomian decomposition method (ADM) are found in [22], Differential transformation method (DTM) [23], Homotopy analysis method (HAM) [24] and the Homotopy perturbation method (HPM) [25]. The VIM is the most effective and convenient one for both weakly and strongly nonlinear equations.…”

Analytic approximate solution of three‐dimensional Navier‐Stokes equations of flow between two stretchable disks

“…In recent years, the HAM has been successfully used to solve many types of nonlinear problems such as the nonlinear equations arising in heat transfer [16], the nonlinear model of diffusion and reaction in porous catalysts [17], the chaotic dynamical systems [18], the nonhomogeneous Blasius problem [19], the generalized three-dimensional MHD flow over a porous stretching sheet [20], the wire coating analysis using MHD Oldroyd 8-constant fluid [21], the axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet [22], the MHD flow of a second grade fluid in a porous channel [23], the generalized Couette flow [24], the squeezing flow between two infinite plates [25], the Glauert-jet problem [26], the Burger and regularized long wave equations [27], the laminar viscous flow in a semiporous channel in the presence of a uniform magnetic field [28], and other problems. All of these successful applications verified the validity, effectiveness, and flexibility of the HAM.…”