Classical explicit finite difference schemes are unsuitable for the solution of the famous Black-Scholes partial differential equation, since they impose severe restrictions on the time step. Furthermore, they may produce spurious oscillations in the solution. We propose a new scheme that is free of spurious oscillations and guarantees the positivity of the solution for arbitrary stepsizes. The...

‎In this paper we propose a numerical scheme to solve the one dimensional nonlinear Klein-Gorden equation‎. ‎We describe the mathematical formulation procedure in details‎. ‎The scheme is three level explicit and based on nonstandard finite difference‎. ‎It has nonlinear denominator function of the step sizes‎. ‎Stability analysis of the method has been given and we prove that the proposed meth...

In previous work we constructed an explicit mapping between large $N$ vector models (free or critical) in $d$ dimensions and a non-local high-spin gravity theory on $AdS_{d+1}$, such that the gravitational reproduces field correlation functions order by $1/N$. this paper discuss three aspects of mapping. First, our original was not valid non-perturbatively $1/N$, since it did include correlatio...

We present an explicit stabilised finite element method for solving Navier-Stokes-Brinkman equations. The proposed algorithm has several advantages. First, the lower equal-order space velocity and pressure is ideal presenting pixel images. Stabilised allows continuity of both tangential normal velocities at interface between regions different micro-permeability or free/porous domain. Second, fu...

this research deals with axial and oblique impact crash tests on simple and hybrid composite tubes. axial and oblique impact tests have been generated on simple and hybrid composite tubes with one, two and three layers. a drop test rig was used to conduct the experiments. furthermore, in order to gain more detailed knowledge about the crash process, finite element simulations of the experiments...