The generalized quasilinearization technique has been employed to obtain a sequence of approximate solutions converging monotonically and rapidly to a solution of the nonlinear Neumann boundary value problem.

In this paper, we present a numerical scheme using uniform Haar wavelet approximation and quasilinearization process for solving some nonlinear oscillator equations. In our proposed work, quasilinearization technique is first applied through Haar wavelets to convert a nonlinear differential equation into a set of linear algebraic equations. Finally, to demonstrate the validity of the proposed m...

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.

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...

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.

The method of Quasilinearization which was developed by Bellman and Kalaba covers the situation when the forcing function is either convex or concave. Here, we describe the process of the Quasilinearization method being extended, refined and generalized so as to include forcing functions which are the sum of a convex and concave function. This includes many special cases which are extensions of...

In this paper the quasilinearization technique along with the Chebyshev polynomials of the first type are used to solve the nonlinear-quadratic optimal control problem with terminal state constraints. The quasilinearization is used to convert the nonlinear quadratic optimal control problem into sequence of linear quadratic optimal control problems. Then by approximating the state and control va...