and Applied Analysis 3 Table 1 Quasilinearization method Integer derivative Caputo’s derivative Monotone sequences Yes Yes Unique solution exists Yes Yes Uniform convergence Yes Yes Quadratic semiquadratic convergence Yes Yes Then, α0 ≤ β0 0, where α0 α0 t t − t0 |t t0 and β0 0 β0 t t − t0 |t t0 imply that α0 t ≤ β0 t , t0 ≤ t ≤ T. Corollary 2.2. The function F t, u σ t u, where σ t ≤ L, is adm...

the purpose of this study is to implement a new modification of the variational iteration method (h-s-vim), which is a combination of spectral method and variational iteration method for heat transfer problems with high nonlinearity order. the merit of this method is that it does not require the solution of any linear or nonlinear system of equations unlike spectral method. furthermore the prop...

We study the existence and approximation of solutions for a nonlinear second order ordinary differential equation with Dirichlet boundary value conditions. We present a generalized quasilinearization technique to obtain a sequence of approximate solutions converging quadratically to a solution.

The behavior of the non-linear-coupled systems arising in axially symmetric hydromagnetics flow between two horizontal plates in a rotating system is analyzed, where the lower is a stretching sheet and upper is a porous solid plate. The equations of conservation of mass and momentum are transformed to a system of coupled nonlinear ordinary differential equations. These equations for the velocit...