A new spectral-homotopy analysis method for solving a nonlinear second order BVP

A modified parametric iteration method for solving nonlinear second order BVPs

“…Example 5.3. As the other example, we consider the following nonlinear second order BVP [9]: where the parameters are selected as in [9], that is, s = F = M = 1.…”

“…Some numerical methods such as finite difference method [4], finite element method [2] and shooting method [8] have been developed for obtaining approximate solutions to BVPs. Recently, much attention has been focused on the analytic or numeric-analytic study of BVPs (e.g., see [6,9] and the references cited therein). Unlike the discrete solutions obtained by the purely numerical methods like the shooting methods, approximate analytical solutions can increase our insights into the natural behavior of complex systems.…”

An improved adaptation of homotopy analysis method

“…Marinca and Herisanu [2] proposed optimal homotopy asymptotic method to investigate the solutions of nonlinear equations arising in heat transfer. Motsa et al [3] introduced a new spectral-homotopy analysis method for solving a nonlinear second order BVP. Homotopy analysis method has been successfully applied to investigate the solutions of integral equations [4].…”

Exact Traveling Wave Solutions for the (1 + 1)-Dimensional Compound KdVB Equation via the Novel (G'/G)-Expansion Method

“…On the other hand, not all equations posed by the advent of NLEEs models are readily solvable. As a result, many original techniques have been successfully urbanized by various groups of researchers, such as the Cole-Hopf transformation method [1], the Miura transformation method [2], the Hirota's bilinear method [3], the ( ) ( ) exp η −Φ -expansion method [4]- [6], the Sumudu transform method [7]- [14], the Fan sub-equation method [15] [16], the spectral-homotopy analysis method [17] [18], the least-squares finite element scheme [19], the (G′/G)-expansion method [20]- [23], the improved (G′/G)-expansion method [24], the trial function method [25], the nonlinear transform method [26], the extended Tanh-function method [27] [28], and the novel (G′/G)-expansion method [29]- [34], homotopy analysis method [35], to name a few. The latter sequence of papers really constituted a ladder honed in the current wealth of repeated experimental and theoretical successes that sprang us to the work at hand, that we hope will greatly benefit the readership, towards the further understanding of NLEEs dynamics and solutions, and mechanisms for recognizing and classifying them.…”