Discrete approximation of the viscous HJ equation

Discrete Approximation of the Riemann Problem for the Viscous Burgers Equation

Approximation of Solitons in the Discrete NLS Equation

We study four different approximations for finding the profile of discrete solitons in the one-dimensional Discrete Nonlinear Schrödinger (DNLS) Equation. Three of them are discrete approximations (namely, a variational approach, an approximation to homoclinic orbits and a Green-function approach), and the other one is a quasi-continuum approximation. All the results are compared with numerical...

The quantum discrete self-trapping equation in the Hartree approximation

We show how the Hartree approximation (HA) can be used to study the quantum discrete self-trapping (QDST) equation, which in turn provides a model for the quantum description of several interesting nonlinear effects such as energy localization, soliton interactions, and chaos. The accuracy of the Hartree approximation is evaluated by comparing results with exact quantum mechanical calculations ...

A continuous approximation fitting to the discrete distributions using ODE

The probability density functions fitting to the discrete probability functions has always been needed, and very important. This paper is fitting the continuous curves which are probability density functions to the binomial probability functions, negative binomial geometrics, poisson and hypergeometric. The main key in these fittings is the use of the derivative concept and common differential ...

Weak Approximation of Cir Equation by Discrete Random Variables

For the CIR equation dXt = (θ − kXt) dt + σ √ Xt dBt, we propose positive weak firstand second-order approximations that use, at each step, generation of discrete (respectively twoand three-valued) random variables (Theorems 3 and 4). The equation is split into deterministic part dDt = (θ − kDt) dt, which is solved exactly, and stochastic part dSt = σ √ St dBt, which is actually approximated in...