there are different commentaries on rumi’s masnavi, each focusing on it from different pints of view such as literary aesthetics, mysticism, philosophy and subject matter. these various commentaries – including those by reynold nicholson, jafar shahidi, mohammad estelami and karim zamani – make their comparison and contrast inevitable. despite their great affinity, they are different from each ...

We compare different solutions of the convection–diffusion–reaction problem with Danckwerts boundary conditions. Analytical solution is found, and method lines Crank–Nicholson are described, applied, compared for values Péclet Damköhler numbers. The eigenvalues eigenfunctions have been obtained all possible dimensionless parameters. And analytical expression concentration has calculated optimum...

In this paper we propose parallel algorithm for the solution of partial differential equations over a rectangular domain using the Crank–Nicholson method by cooperation with the DuFort–Frankel method and apply it on a model problem, namely, the heat conduction equation. One of the well known parallel techniques in solving partial differential equations in cluster computing environment is the do...

The paper presents a numerical study of the periodic self focusing behavior of a laser pulse propagation in a gas filled capillary plasma with a parabolic electron density profile. An implicit and inherently stable Crank-Nicholson method was used to demonstrate the periodic laser beam waist behavior inside the tube discharge. The dependence of the tube radius and beam waist on maximum intensity...

Many temporal discretization methods for linear evolution equations converge uniformly on compact time intervals at the rate 1 nα only for sufficiently smooth initial data. It is shown that these methods can be regularized such that the new schemes converge ‘in the average’ at the rate 1 nα for all initial data. Examples given include the Crank-Nicholson scheme and the alternating direction imp...

The finite-difference beam propagation method based on the Douglas scheme is extended to a nonuniform grid. The truncation error is reduced to ~ ( A z ) ~ , provided the grid growth factor is r = 1 + ~ ( A z ) , while maintaining a tridiagonal matrix. The numerical results show that the accuracy is improved as compared with that obtained from the conventional nonuniform Crank-Nicholson scheme. ...

In the final chapter, Nicholson uses the scenario planning method to explore several possible futures for digital reference services. Using two dimensions – funding sources and automation four different scenarios are developed. Common needs across all four scenarios drive a discussion of both current and future research needs, and are used to position all components from this digital reference ...

inger equation (TDSE). It uses the Crank–Nicholson scheme to propthen solving the resulting eigenproblem by expanding on agate the wavefunction forward in time and finite differences to some basis set. Examples of such techniques are the colloapproximate the derivative operators. The resulting sparse linear cation and Galerkin methods implemented via piecewise system is solved by the symmetric ...