Recently, multi-time stepping methods have become very popular among scientist due to their high stability in problems with critical conditions. One important shortcoming of these methods backs to their high amount of uncontrolled amplitude decay. This study proposes a new multi-time stepping method in which the time step is split into two sub-steps. The first sub-step is solved using the well-...

In this paper, we consider the problem of computing numerical solutions for stochastic differential equations (SDEs) of Itô form. A fully explicit method, the split-step forward Milstein (SSFM) method, is constructed for solving SDEs. It is proved that the SSFM method is convergent with strong order γ = 1 in the mean-square sense. The analysis of stability shows that the mean-square stability p...

in this paper, exact solution for two-plane transverse vibration analysis of axial-loaded multi-step timoshenko rotor carrying concentrated masses is presented. each attached element is considered to have both translational and rotational inertia. forward and backward frequencies and corresponding modes are obtained using transfer matrix method (tmm). the effect of the angular velocity of spin,...

The computer program spip is aimed at solving the Generalized Non-Linear Schrödinger equation (GNLSE), involved in optics e.g. in the modelling of light-wave propagation in an optical fibre, by the Interaction Picture method, a new efficient alternative method to the Symmetric Split-Step method. In the spip program a dedicated costless adaptive step-size control based on the use of a 4th order ...

BACKGROUND Radio frequency ablation (RFA) has been accepted clinically as a useful local treatment for hepatocellular carcinoma (HCC). However, intrahepatic recurrence after RFA has been reported which might be attributable to increase in intra-tumor pressure during RFA. To reduce the pressure and ablation time, we developed a novel method of RFA, a multi-step method in which a LeVeen needle, a...

In this work we develop a new optimal without memory class for approximating a simple root of a nonlinear equation. This class includes three parameters. Therefore, we try to derive some with memory methods so that the convergence order increases as high as possible. Some numerical examples are also ‎presented.‎‎