Linear and Non-linear difference equations are appeared in many fields of applied mathematics, engineering and physical problems such as natural phenomena, social and economical systems which have essentially discrete elements. In this paper by making use of invariant functions for discrete derivatives [6], we present an analytical method to solve the general form of the n-th order non-homogeno...

We apply the concept of Asymptotic Preserving (AP) schemes [14] to the linearized p−system and discretize the resulting elliptic equation using standard continuous Finite Elements instead of Finite Differences. The fully discrete method is analyzed with respect to consistency, and we compare it numerically with more traditional methods such as Implicit Euler’s method.

We discuss the application of the finite element method to the numerical solution of scalar two–dimensional steady convection–diffusion equations with the emphasis on upwinding techniques satisfying the discrete maximum principle. Numerical experiments in convection–dominated case indicate that the improved Mizukami–Hughes method is the best choice for solving the mentioned class of problems us...

This paper describes the recently developed mixed mimetic spectral element method for the Stokes problem in the vorticity-velocity-pressure formulation. This compatible discretization method relies on the construction of a conforming discrete Hodge decomposition, that is based on a bounded projection operator that commutes with the exterior derivative. The projection operator is the composition...

In this paper, we propose a Newton-Krylov solver and a Picard-Krylov solver for finite element discrete problem of stationary incompressible magnetohydrodynamic equations in three dimensions. Using a mixed finite element method, we discretize the velocity and the pressure by H1(Ω)-conforming finite elements and discretize the magnetic field by H(curl,Ω)-conforming edge elements. An efficient pr...

In this paper a new concept, spatio-temporal generalized frequency response functions (STGFRF), is introduced for the first time to characterize nonlinear spatio-temporal dynamical systems in the frequency domain. A probing method is developed to calculate the STGFRFs recursively for both continuous and discrete spatio-temporal systems. The algorithm is computationally compact and exposes the e...

This paper proposes a novel method for the optimal parameter selection of the discrete-time switch model used in circuit solvers that adopt the fixed admittance matrix nodal method (FAMNM) approach. As known, FAMNM-based circuit solvers allow to reach efficient computation times, in particular for realtime simulation applications, since they do not need the inversion of the circuit nodal admitt...

we describe how to obtain electronic transport properties of disordered graphene, including the tight binding model and nearest neighbor hopping. we present a new method for computing, electronic transport wave function and greens function of the disordered graphene. in this method, based on the small rectangular approximation, break up the potential barriers in to small parts. then using the f...