Copyright q 2012 I. Yermachenko and F. Sadyrbaev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. An equation d/dt Φ t, x′ f t, x 0 is considered together with the boundary conditions Φ a, x′ a 0, x b 0. This problem under appropr...

In this paper, we propose a method for solving some classes of the singular fractional nonlinear Lane-Emden type equations. The is proposed by utilizing second-kind Chebyshev wavelets in conjunction with quasilinearization technique. operational matrices are used. tested on standard equation, isothermal gas spheres and other examples. We compare results produced present well-known to show accur...

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...

We propose a new modification of Bellman’s quasilinearization method such that at any iteration step, it works with an approximate solution of the original nonlinear system and with new approximation of parameters α(k+1) which are close enough to the previous ones. As an output, this approach provides a construction of a convergent sequence of parameters where the limit is the best approximatio...

In the spotlight of this study is a particular type of first order dynamic initial value problem of the form u = f(t, u) + g(t, u), u(t0) = u0, where f, g ∈ Crd [T × R,R] are nondecreasing and nonincreasing in u, respectively. A quasilinearization technique utilizing the nature of natural lower and upper solutions as well as coupled lower and upper solutions is developed for this problem. Begin...

Despite the availability of an abundant literature on singularly perturbed problems, interest toward non-linear problems has been limited. In particular, parameter-uniform methods for semilinear are quasi-non-existent. this article, we study a two-dimensional convection-diffusion problems. Our approach requires linearization continuous problem using quasilinearization technique. We then discret...

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...