In this paper we present the methods of Quasilinearization and Generalized Quasilinearization for hybrid Caputo fractional differential equations which are Caputo fractional differential equations with fixed moments of impulse. In order to prove this results we use the weakened assumption of -continuity in place of local Hölder continuity.

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.

The method of generalized quasilinearization for second-order boundary value problems has been extended when the forcing function is the sum of 2-hyperconvex and 2-hyperconcave functions. We develop two sequences under suitable conditions which converge to the unique solution of the boundary value problem. Furthermore, the convergence is of order 3. Finally, we provide numerical examples to sho...

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 we improve the quasilinearization method by barycentric Lagrange interpolation because of its numerical stability and computation speed to achieve a stable semi analytical solution. Then we applied the improved method for solving the Fin problem which is a nonlinear equation that occurs in the heat transferring. In the quasilinearization approach the nonlinear differential equatio...

GENERALIZED QUASILINEARIZATION METHOD FOR COINCIDENCES WITH APPLICATIONS TO ELLIPTIC BOUNDARY VALUE PROBLEMS

‎The ‎method ‎of ‎quasilinearization ‎is ‎an ‎effective ‎tool ‎to ‎solve nonlinear ‎equations ‎when ‎some ‎conditions‎ on ‎the ‎nonlinear term ‎of ‎the ‎problem ‎are ‎satisfi‎‎ed. ‎W‎hen ‎the ‎conditions ‎hold, ‎applying ‎this ‎techniqu‎e ‎gives ‎two ‎sequences of ‎coupled ‎linear ‎equations‎ and ‎the ‎solutions ‎of ‎th‎ese ‎linear ‎equations ‎are quadratically ‎convergent ‎to ‎the ‎solution ‎o...