A hybrid method to model the shear wave (SH) scattering from 2D fractures embedded in a heterogeneous medium is developed by coupling Boundary Element Method (BEM) and Finite Different Method (FDM) in the frequency domain. FDM is used to propagate an SH wave from a source through heterogeneities to localized homogeneous domains where fractures are embedded within artificial boundaries. Accordin...

Two new finite difference schemes based on the method of characteristics are presented for convection-diffusion problems. Both of the schemes are of second order in time, and the matrices of the derived systems of linear equations are symmetric. No numerical integration is required for them. The one is of first order in space and the other is of second order. For the former scheme, an optimal e...

This paper investigates some fourth-order accurate explicit finite difference schemes for the 2-D wave equation obtained using 13-, 17-, 21-, and 25-point discrete Laplacians. Optimisation is conducted in order to minimise numerical dispersion and computational costs. New schemes are presented that are more computationally efficient than nine-point explicit schemes at maintaining less than one ...

Future architectures designed to deliver exascale performance motivate the need for novel algorithmic changes in order to fully exploit their capabilities. In this paper, the performance of several numerical algorithms, characterised by varying degrees of memory and computational intensity, are evaluated in the context of finite difference methods for fluid dynamics problems. It is shown that, ...

1School of Science, Beijing Jiaotong University, Beijing 100044, People’s Republic of China 2Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, People’s Republic of China 3School of Mathematics and Physics, North China Electric Power University, Beijing 102206, People’s Republic of China 4Department of Scientific Computing, Florida State University, Dirac Sci. Lib. B...

We derive high-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids. The schemes are fourth-order accurate in space and secondorder accurate in time for vanishing correlation. In our numerical study we obtain highorder numerical convergence also for non-zero correlation and non-smooth payoffs which are typical in option pricing. In all ...

We discuss an initial value problem for an implicit second order ordinary differential equation which arises in models of flow in concrete. Depending on the initial condition, the solution features a sharp interface with derivatives which become numerically unbounded. By using an integrator based on finite difference methods and equipped with adaptive step size selection, it is possible to comp...

An external barrier of an option contract is a stochastic variable which determines whether the option is knocked in or out when the value of the variable is above or below some predetermined level, but itself is not the price of an asset which underlies the option. In this paper, we present analytic formulation for the valuation of European options on one or multiple assets with single externa...

In the research, special type of linear volterra integro-differential equations is considered. This paper compares the Homotopy perturbation method (HPM) with finite difference method for solving these equations. HPM is an analytical procedure for finding the solutions of problems which is based on the constructing a Homotopy with an imbedding parameter p that is considered as a small parameter...

This work overcomes the difficulty of dealing with large curvatures in a high order matched interface and boundary (MIB) method proposed for solving elliptic interface problems. The MIB method smoothly extends the solution across the interface so that standard high order central finite difference schemes can be used without the loss of accuracy. One feature of the MIB is that it disassociates t...