The Maxwell equations are solved by a long-stencil fourth order finite difference method over a Yee grid, in which different physical variables are located at staggered mesh points. A careful treatment of the numerical values near the boundary is introduced, which in turn leads to a “symmetric image” formula at the “ghost” grid points. Such a symmetric formula assures the stability of the bound...

In this paper three pairs of embedded Runge–Kutta type methods for directly solving special third order ordinary differential equations (ODEs) of the form denoted as RKD methods are presented. The first is the RKD4(3) pair which is third order embedded in fourth-order method has the property first same as last (FSAL) whereby the last row of the coefficient matrix is equal to the vector output. ...

We present a numerical approach for generalised Korteweg-de Vries (KdV) equations on the real line. In spatial dimension we compactify line and apply Chebyshev collocation method. The time integration is performed with an implicit Runge-Kutta method of fourth order. Several examples are discussed: initial data bounded but not vanishing at infinity as well satisfying Faddeev condition, i.e. slow...

In this work, a novel mathematical model of Coronavirus (2019-nCov) with general population mask use modified parameters. The proposed consists fourteen fractional-order nonlinear differential equations. Grünwald-Letnikov approximation is used to approximate the new hybrid fractional operator. Compact finite difference method six order operator developed study model. Stability analysis methods ...

An embedded diagonally implicit Range-Kutta Nystrom (RKN) method is constructed for the integration of initial value problems for second order ordinary differential equations possessing oscillatory solutions. This embedded method is derived using a three stage diagonally implicit Runge-Kutta Nystrom method of order four within which a third order three stage diagonally implicit Runge-Kutta Nyst...

this paper addresses the combined effects of couple stresses, thermal radiation, viscous dissipation and slip condition on a free convective flow of a couple stress fluid induced by a vertical stretching sheet. the cogley- vincenti-gilles equilibrium model is employed to include the effects of thermal radiation in the study. the governing boundary layer equations are transformed into a system o...

A meshless numerical technique is proposed for solving the generalized variable coefficient Schrodinger equation and Schrodinger-Boussinesq system with electromagnetic fields. The employed meshless technique is based on a generalized smoothed particle hydrodynamics (SPH) approach. The spatial direction has been discretized with the generalized SPH technique. Thus, we obtain a system of ordinary...

This study proposes a new linear approximation for solving the dynamic response equations of a rocking rigid block. Linearization assumptions which have already been used by Hounser and other researchers cannot be valid for all rocking blocks with various slenderness ratios and dimensions; hence, developing new methods which can result in better approximation of governing equations while keepin...

We analyze explicit Runge–Kutta schemes in time combined with stabilized finite elements in space to approximate evolution problems with a first-order linear differential operator in space of Friedrichs-type. For the time discretization, we consider explicit secondand third-order Runge–Kutta schemes. We identify a general set of properties on the spatial stabilization, encompassing continuous a...

In this paper, we propose a high order Galerkin discretization scheme for solving steady compressible Navier-Stokes equations. The pointwise numerical fluxes are separated into convective fluxes, acoustic fluxes, and viscous fluxes. The separation of convective flux and viscous flux is to avoid round off errors. The separation of the acoustic flux is due to non-central scheme employed near the ...