Optimized Finite Difference Formulas for Accurate High Frequency Components

Accurate Finite Difference Methods for Option Pricing

Calculation of Weights in Finite Difference Formulas∗

The classical techniques for determining weights in finite difference formulas were either computationally slow or very limited in their scope (e.g., specialized recursions for centered and staggered approximations, for Adams–Bashforth-, Adams–Moulton-, and BDF-formulas for ODEs, etc.). Two recent algorithms overcome these problems. For equispaced grids, such weights can be found very convenien...

On the Wavelet Optimized Finite Difference Method

When one considers the e ect in the physical space, Daubechies-based wavelet methods are equivalent to nite di erence methods with grid re nement in regions of the domain where small scale structure exists. Adding a wavelet basis function at a given scale and location where one has a correspondingly large wavelet coe cient is, essentially, equivalent to adding a grid point, or two, at the same ...

Finite-difference Modeling of High-frequency Rayleigh waves

The finite-difference (FD) method described here is specially developed to model high-frequency Rayleigh-wave propagation in near-surface mediums. Although many FD programs existed for earthquake research and oil exploration, none has been developed to model high-frequency Rayleigh-wave propagation in near-surface elastic mediums when the source and all receivers are on the free-surface. The sc...

Nonstandard finite difference schemes for differential equations

In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs). Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with ...