The method of quasilinearization coupled with the method of lower and upper solutions is applied to systems of nonlinear differential equations with a singular matrix. It generates sequences of approximate solutions which are convergent to the solution and the convergence is quadratic or semiquadratic.

The quasilinearization method coupled with the method of upper and lower solutions is used for a class of nonlinear boundary value problems with integral boundary conditions. We obtain some less restrictive sufficient conditions under which corresponding monotone sequences converge uniformly and quadratically to the unique solution of the problem. An example is also included to illustrate the m...

The method of upper and lower solutions and the method of quasilinearization for a second order nonlinear differential equation −x (t) = f (t, x, x ), t ∈ [0, 1] subject to the separated boundary conditions p0x(0) − q0x (0) = a, p1x(1) + q1x (1) = b, is developed. A monotone sequence of solutions of linear problems converging uniformly and quadratically to a solution of the problem is obtained....

In this paper, the boundary layer flow of an Eyring-Powell non-Newtonian fluid over a linearly stretching sheet is solved using the combination of the quasilinearization method and the Fractional order of Rational Chebyshev function (FRC) collocation method on a semi-infinite domain. The quasilinearization method converts the equation into a sequence of linear equations then, using the FRC coll...

The method of upper and lower solutions and quasilinearization for nonlinear singular equations of the type −x(t) + λx(t) = f(t, x(t)), t ∈ (0, 1), subject to nonlocal three-point boundary conditions x(0) = δx(η), x(1) = 0, 0 < η < 1, are developed. Existence of a C1 positive solution is established. A monotone sequence of solutions of linear problems converging uniformly and rapidly to a solut...

Advances in automatic control theory may be seen to have two main objectives the synthesis of improved controllers for a given plant and the extension of the range of plants considered for control. Optimal control theory and its application to linear stems is an example of the former, whilst advances in the latter have been largely concerned with describing-function and quasilinearization techn...

In this paper we consider the nonlinear parabolic integro-differential equation with initial and boundary conditions. We develop the method of generalized quasilinearization to generate linear iterates that converge quadratically to the unique solution of the nonlinear parabolic integro-differential equation. For this purpose, we establish comparison results for the parabolic integro-differenti...

The generalized quasilinearization method for second-order boundary value problem has been extended when the forcing function is the sum of two functions without require that any of the two functions involved to be 2-hyperconvex or 2-hyperconcave. Two sequences are developed under suitable conditions which converge to the unique solution of the boundary value problem. Furthermore, the convergen...