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...

We investigate entropy generation in unsteady three-dimensional axisymmetric MHD nanofluid flow over a non-linearly stretching sheet. The flow is subject to thermal radiation and a chemical reaction. The conservation equations were solved using the spectral quasi-linearization method. The novelty of the work is in the study of entropy generation in three-dimensional axisymmetric MHD nanofluid a...

In this article, we present a simple direct matrix method for analytically computing the Jacobian of nonlinear algebraic equations that arise from the discretization of nonlinear integrodifferential equations. This method is based on a formulation of the discretized equations in vector form using only matrix-vector products and component-wise operations. By applying simple matrixbased different...

We discuss the existence and uniqueness of the solutions of a second-order m-point nonlocal boundary value problem by applying a generalized quasilinearization technique. A monotone sequence of solutions converging uniformly and quadratically to a unique solution of the problem is presented.

We apply the generalized quasilinearization technique to obtain a monotone sequence of iterates converging quadratically to the unique solution of a general second order nonlinear differential equation with nonlinear nonlocal mixed three-point boundary conditions. The convergence of order n (n ≥ 2) of the sequence of iterates has also been established.