Investigation of a powerful analytical method into natural convection boundary layer flow

Homotopy analysis method for multiple solutions of the fractional Sturm-Liouville problems

“…According to boundary conditions (13) and the rule of solution expression (15), it is straightforward that the initial approximations should be in the form u 0 (x) = x, and we have the zero-order deformation equation (1) with the initial conditions φ(0; p) = 0.…”

“…Zurigat et al [10] applied the HAM for handling systems of fractional differential equations. The technique employed here is very powerful and has been already successfully applied to various complicated problems [11][12][13][14][15][16][17][18][19][20][21].…”

Chebyshev collocation spectral method simulation for the 2D boundary layer flow and heat transfer in variable viscosity MHD fluid over a stretching plate

“…differential equations (ODEs) using a similarity transformation by introducing a set of similarity variables [25][26][27] or picking up the method of Lie group method [19,[28][29][30][31]. Instead of adopting similarity transformation to simplify the non-linear PDEs into the ODEs as a sort of the one dimensional analysis, another feasible way to deal with the original governing equations is to transform them into a system of non-dimensional differential equations by introducing the variable transformation.…”

Analytical Solution For Nnonlinear Vibration Of Micro-electromechanical System (mems) By Frequency-amplitude Formulation Method

“…Therefore special techniques should be applied to solve them. Many of these techniques have been performed in recent literatures such as Homotopy Perturbation Method (HPM) [14][15][16][17][18], Homotopy Analysis Method (HAM) [19][20][21], Iteration Perturbation Method (IPM) [22][23][24], Variational Iteration Method (VIM) [25][26][27][28], Differential Transformation Method (DTM) [29][30], Frequency Amplitude Formulation (FAF) [31][32][33], Max-Min Approach (MMA) [34][35][36][37][38].…”