The application of the finite difference method to discretize the complex Helmholtz equation on a bounded region in the plane produces a linear system whose coefficient matrix is block tridiagonal and is some (complex) perturbation of an M-matrix. The matrix is also complex symmetric, and its real part is frequently indefinite. Conjugate gradient type methods are available for this kind of line...

Particle-in-cell (PIC) methods allow the study of plasma behavior by computing the trajectories of finite-size particles under the action of external and self-consistent electric and magnetic fields defined in a grid of points. In this work, the Finite Element Method (FEM) is used in order to obtain the self-consistent fields. An electrostatic PIC-FEM computational code for simulation of one-di...

In this article, qualitative longitudinal (QL) research is presented as a powerful form of fluid enquiry. The combination its real-world and real-time features enables methodology to ‘follow reality in all windings’, and, thereby, produce useful knowledge for policy professional practice. main focus on the power QL illuminate complex causal processes by teasing out their multiple, relational el...

the idea of difference sequences of real (or complex) numbers was introducedby ki zmaz cite{kizmaz}. in this paper, using the difference operator and alacunary sequence, we introduce and examine the class of sequence $bv_{theta}left(  delta,mathcal{f}right)  .$ we study some of its properties likesolidity, symmetricity, etc.