Now-a-days computational fluid mechanics has become very vital area in which obtained governing equations are differential equations. Sometimes, these governing equations cannot be easily solved by existing analytical methods. Due to this reason, we use various numerical techniques to find out approximate solution for such problems. Among these techniques, finite volume method is also being use...

We propose a new high-order alternating direction implicit (ADI) finite difference scheme for the solution of initial-boundary value problems of convection-diffusion type with mixed derivatives and non-constant coefficients, as they arise from stochastic volatility models in option pricing. Our approach combines different high-order spatial discretisations with Hundsdorfer and Verwer’s ADI time...

We prove the nonlinear stability and convergence of a fully discrete, pseudospectral scheme for the "good" Boussinesq equation un = -uxxxx + uxx + ("2)xx ■ Numerical comparisons with finite difference schemes are also reported.

We study a unidirectional hyperbolic transport equation, with a homogeneous stochastic transport velocity, solved by Monte Carlo simulation. Several finite difference schemes are applied to the deterministic problem in each Monte Carlo iteration, and the numerical solution of the stochastic problem is compared to analytical solutions derived in the paper. We present both a theoretical analysis ...

A new method modifying the frequency dependent alternating direction implicit finite difference time domain (FD–ADI– FDTD) is presented. The method can improve the accuracy of FD–ADI–FDTD without significant increase of computational costs. The proposed method is validated by numerical tests. Index Terms ADI–FDTD, Debye media, Accuracy of FDTD

An elliptic system of M(≥ 2) singularly perturbed linear reactiondiffusion equations, coupled through their zero-order terms, is considered on the unit square. This system does not in general satisfy a maximum principle. It is solved numerically using a standard difference scheme on tensor-product Bakhvalov and Shishkin meshes. An error analysis for these numerical methods shows that one obtain...

In the present manuscript we consider the practical problem of wave interaction with a vertical wall. However, the novelty here consists in the fact that the wall can move horizontally due to a system of springs. The water wave evolution is described with the free surface potential flow model. Then, a semi-analytical numerical method is presented. It is based on a mapping technique and a finite...

This paper is devoted to the numerical comparison of methods applied to solve problems with nonlocal boundary conditions. Four numerical methods are compared, namely, finite differences method, Galerkin method, Keller Box scheme and orthogonal spline collocation method. Mathematics Subject Classification: 74S05, 74S20, 74S30, 74H15

In this work, we introduce new finite-difference shock-capturing central schemes on staggered grids. Staggered schemes may have better resolution of the corresponding unstaggered schemes of the same order. They are based on high order non oscillatory reconstruction (ENO or WENO), and a suitable ODE solver for the computation of the integral of the flux. Although they suffer from a more severe s...

SUMMARY Metamaterials are generally defined as a class of artificial effective media which macroscopically exhibit extraordinary electromagnetic properties that may not be found in nature, and are composed of periodically structured dielectric, or magnetic, or metallic materials. This paper reviews recently developed electromagnetic modeling methods of metama-tericals and their inherent basic i...