We study a decoupling iterative algorithm based on domain decomposition for the time-dependent nonlinear Stokes–Darcy model, in which different time steps can be used flow region and porous medium. The coupled system is formulated as space-time interface problem condition mass conservation. then solved by nested iteration approach involves, at each Newton iteration, solution of linearized and, ...

The integrating factor technique is widely used to solve numerically (in particular) the Schrödinger equation in context of spectral methods. Here, we present an improvement this method exploiting freedom provided by gauge condition potential. Optimal conditions are derived considering and temporal numerical resolution with adaptive embedded scheme arbitrary order. We illustrate approach nonlin...

In this paper, we investigate the connection between closed Newton-Cotes formulae, trigonometrically-fitted methods, symplectic integrators and efficient integration of the Schr¨odinger equation. The study of multistep symplectic integrators is very poor although in the last decades several one step symplectic integrators have been produced based on symplectic geometry (see the relevant lit...

We present a modified version of the infeasible-interior- We present a modified version of the infeasible-interior-point algorithm for monotone linear complementary problems introduced by Mansouri et al. (Nonlinear Anal. Real World Appl. 12(2011) 545--561). Each main step of the algorithm consists of a feasibility step and several centering steps. We use a different feasibility step, which tar...