This article proposes a family of non-standard methods coupled with compact finite differences to numerically integrate the non-linear Burgers’ equation. Firstly, is derived deal system ordinary differential equations (ODEs) arising from semi-discretization initial-boundary value partial (PDEs). Further, method this considered as special case and fourth-order difference resulting in combined nu...

Computational aeroacoustics often use finite difference schemes optimized to require relatively few points per wavelength; such optimized schemes are often called Dispersion Relation Preserving (DRP). Similar techniques are also used outside aeroacoustics. Here the question is posed: what is the equivalent of points per wavelength for growing or decaying waves, and how well are such waves resol...

A new method combining a finite difference method and a reduced order model (ROM) algorithm is presented for twodimensional (2-D) electromagnetic problems. The problem space is subdivided into subdomains of a generic type. By discretizing the spatial derivatives in a way similar to the finite-difference in time-domain technique (FDTD), the state equations are written down in each subdomain. Fro...

The cervix is a biochemically active tissue that changes its biomechanical properties in a remodeling process during pregnancy to be prepared for parturition. This maturation process is associated with changes of the mechanical properties of the cervical stroma. Preterm delivery is connected with undesired cervical changes bound to cervical ripening. Non-destructive evaluation using ultrasonic ...

Knowledge and control of residual strain is critical for device design in MEMS, and therefore it is important to establish standards for residual strain measurement. In this study, pointer, microring, bent-beam, and fixed-fixed beam test structures are used to evaluate residual strain both theoretically and experimentally. An equation that enables easier evaluation of bentbeam structures is der...

In this paper, we derive a discretized multi-group epidemic model with time delay by using a nonstandard finite difference (NSFD) scheme. A crucial observation regarding the advantage of the NSFD scheme is that the positivity and boundedness of solutions of the continuous model are preserved. Furthermore, we show that the discrete model has the same equilibria, and the conditions for their stab...

The space and time discretization inherent to all FDTD schemes introduce non-physical dispersion errors, i.e. deviations of the speed of sound from the theoretical value predicted by the governing Euler differential equations. A general methodology for computing this dispersion error via straightforward numerical simulations of the FDTD schemes is presented. The method is shown to provide remar...

unsteady flow through non - homogeneous and anisotropic porous media can be modeled by a partial differential equation.' this-equation cannot be solved analytically. hence, numerical methods. such as the finite element and the finite difference methods might be employed. in this study a mathematical model has been developed using the fully implicit finite difference method with control vol...

in this paper, the temperature distribution around a moving heat source had been investigated including the phase change and non phase change . in non-phase change state, the governing equation was converted to finite difference equation by finite volume method and the equation was solved by alternating direction implicit method. this method was unconditionally stable . in phase change state, t...