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...

*Correspondence: [email protected] 1College of Electronic and Information Engineering, Hebei University, Baoding, 071002, China Full list of author information is available at the end of the article Abstract In this paper, by using the method of quasilinearization to discuss the periodic boundary value problem for a nonlinear singular differential system with ‘maxima’, we obtain monotone iterat...

On the background of a careful analysis of linear DAEs, linearizations of nonlinear index2 systems are considered. Finding appropriate function spaces and their topologies allows to apply the standard Implicit Function Theorem again. Both, solvability statements as well as the local convergence of the Newton-Kantorovich method (quasilinearization) result immediately. In particular, this applies...

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 analysis of heat conduction through a solid with heat generation leads to a linear matrix differential equation with separated boundary conditions. We present a symmetric second order exponential integrator for the numerical integration of this problem using the imbedding formulation. An algorithm to implement this explicit method in an efficient way with respect to the computational cost o...