[en] The phenomenon of choking which is observed for compressible flows is mathematically interpreted as the characteristic determinant of the flow equations being zero. If it is computed by a finite difference method, it is shown that a flow rate blockage results from a property of the matrix of the linearized finite difference equations. This property is reducibility

No abstract available

[en] Some useful ways of improving the speed and accuracy of finite-difference methods for eigenvalue calculations are proposed and are tested successfully on several problems, including one for which the potential is highly singular at the origin. (author)

[en] Ferrite has a variety of applications in accelerator components, and the capability to model this magnetic material in the time domain is an important adjunct to currently available accelerator modeling tools. In this paper is described a general dispersive material model which is suitable for a wide variety of media, including ferrite. Based on this model we have developed a representation of the time-domain magnetic properties of PE11BL, the ferrite used in the induction modules of the ETA-II (Experimental Test Accelerator -II) induction linac at LLNL. This material is characteristic of the soft ferrites commonly used in induction accelerators. The model has been implemented in 1-D and 2-D finite-difference time-domain (FDTD) electromagnetic simulators, and comparisons with analytic and experimental results are presented. (Author) tab., 6 figs., 11 refs

[en] This report summarizes work in our analytical investigation of explosions inside a flow network, which emphasizes the explosive event itself. A special finite-difference scheme known as Flux-Corrected Transport has been adapted to solve gas-dynamic problems with large flow gradients, including shocks and contact surfaces. The results of this work can be used to supply the source or driving force for our far-field analysis. A sample model of the problem of shock and contact surface propagation is presented

[en] A new finite-difference method for the numerical solution of gas dynamics equations is proposed. This method is a uniform monotonous finite-difference scheme of second-order approximation on time and space outside of domains of shock and compression waves. This method is based on inputting adaptive artificial viscosity (AAV) into gas dynamics equations. In this paper, this method is analyzed for 2D geometry. The testing computations of the movement of contact discontinuities and shock waves and the breakup of discontinuities are demonstrated.

[en] Highlights: • Financial models for awareness and trial. • The nonstandard finite difference method. • The Jacobi–Gauss–Lobatto spectral collocation method (collocation method. • Positivity and boundedness of a scheme. - Abstract: In this paper, two numerical techniques are introduced to study numerically the general fractional advertising model. This system describes the flux of the consumers from unaware individuals group to aware or purchased group. The first technique is an asymptotically stable difference scheme, which was structured depending on the nonstandard finite difference method. This scheme preserves the properties of the solutions of the model problem as the positivity and the boundedness. The second technique is the Jacobi–Gauss–Lobatto spectral collocation method which is exponentially accurate. By means of this approach, such problem is reduced to solve a system of nonlinear algebraic equations and are greatly simplified the problem. Numerical comparisons to test the behavior of the used techniques are run out. We conclude from the computational work that: the Jacobi–Gauss–Lobatto spectral collocation method is more accurate whereas the nonstandard finite difference method requires less computational time.

[en] Highlights: • Local spatio-temporal refinement for the Finite Difference Time Domain algorithm. • Locally reduced space step with locally reduced time step. • The refinement scheme is explicit and provably conditionally stable. • Refinement by arbitrary powers of 2 is possible. In this paper we introduce an explicit and provably conditionally stable Finite Difference Time Domain (FDTD) algorithm for Maxwell's equations, with local refinement in both the spatial discretization length and in the time step (spatiotemporal refinement). This enables local spatial refinement with a locally reduced time step.

[en] The Burgers equation is considered. The equation is solved using finite difference methods. The standard finite difference method may lead to inaccurate solutions, unless a very fine mesh is used, which results in expensive computations. Therefore, we implement an adaptive finite difference moving mesh method as an alternative numerical method to solve the equation. The advantages of implementing the adaptive method are investigated. (paper)

[en] Highlights: • We develop a method to compute the parameters of the CEV model implied by American options. • This is the first procedure for calibrating the CEV model to American option prices. • The proposed approach is extensively tested on the NYSE market. • The novel method turns out to be very efficient in computing the CEV model parameters. • The CEV model provides only a marginal improvement over the lognormal model. - Abstract: We develop a highly efficient procedure to forecast the parameters of the constant elasticity of variance (CEV) model implied by American options. In particular, first of all, the American option prices predicted by the CEV model are calculated using an accurate and fast finite difference scheme. Then, the parameters of the CEV model are obtained by minimizing the distance between theoretical and empirical option prices, which yields an optimization problem that is solved using an ad-hoc numerical procedure. The proposed approach, which turns out to be very efficient from the computational standpoint, is used to test the goodness-of-fit of the CEV model in predicting the prices of American options traded on the NYSE. The results obtained reveal that the CEV model does not provide a very good agreement with real market data and yields only a marginal improvement over the more popular Black–Scholes model.