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 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...

The effects of thermal conductivity which depend on temperature are conversely proportional with the linear function free convective flow where fluid is viscous and incompressible along a heated uniform vertical wavy surface has been examined in this study. boundary layer equations associated conditions that govern converted into nondimensional form by using an appropriate transformation. In do...

In this paper, the weighted average-based differential quadrature method is presented for solving one-dimensional homogeneous first-order non-linear parabolic partial equation. First, given solution domain discretized by using uniform discretization grid point. Next, Taylor series expansion we obtain central finite difference of equation involving with temporal variable associated average deriv...