A generalized quasilinearization technique is developed to obtain a sequence of approximate solutions converging monotonically and quadratically to a unique solution of a boundary value problem involving Duffing type nonlinear integro-differential equation with integral boundary conditions. The convergence of order k k ≥ 2 for the sequence of iterates is also established. It is found that the w...

SUMMARY Health monitoring of structural systems for the detection of damage is a critical practice in determining their safety and service life. A large amount of research has been done in applying damage detection analysis to linear models of structures. Although many real structures exhibit nonlinear behavior prior to or as a result of damage, there are currently few tools to apply damage det...

In this paper, singularly perturbed quasilinear boundary value problems are taken into account. With purpose, a finite difference scheme is proposed on Shishkin-type mesh (S-mesh). Quasilinearization technique and interpolating quadrature rules used to establish the numerical scheme. Then, an error estimate derived. A experiment demonstratedto verify theory.

In this paper, we propose quasilinearization methods that convert nonlocal fully-nonlinear parabolic systems into the quasilinear systems. The serve as important mathematical tools for modelling subgame perfect equilibrium solutions to time-inconsistent dynamic choice problems, which are motivated by study of behavioral economics. Different types were studied but left behind case and connection...

We propose a sequence of highly accurate higher order convergent iterative schemes by embedding the quasilinearization algorithm within a spectral collocation method. The iterative schemes are simple to use and significantly reduce the time and number of iterations required to find solutions of highly nonlinear boundary value problems to any arbitrary level of accuracy. The accuracy and converg...

The object of investigation of the paper is a special type of difference equations containing the maximum value of the unknown function over a past time interval. These equations are adequate models of real processes which present state depends significantly on their maximal value over a past time interval. An algorithm based on the quasilinearization method is suggested to solve approximately ...