The method of upper and lower solutions and the generalized quasilinearization technique for second-order nonlinear m-point dynamic equations on time scales of the type xΔΔ t f t, x , t ∈ 0, 1 T 0, 1 ∩ T, x 0 0, x σ2 1 ∑m−1 i 1 αix ηi , ηi ∈ 0, 1 T, ∑m−1 i 1 αi ≤ 1, are developed. A monotone sequence of solutions of linear problems converging uniformly and quadratically to a solution of the pro...

The method of generalized quasilinearization technique when is applied to the nonlinear integrodifferential equations of Volterra type, gives two sequences of linear integro-differential equations with solutions monotonically and quadratically convergent to the solution of nonlinear equation. In this paper we employ step-by-step collocation method to solve the linear equations numerically and t...

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.

Optimal boundary control of semilinear parabolic equations requires efficient solution methods in applications. Solution methods bypass the nonlinearity in different approaches. One approach can be quasilinearization (QL) but its applicability is locally in time. Nonetheless, consecutive applications of it can form a new method which is applicable globally in time. Dividing the control problem ...

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...