Computing derivatives by finite-difference approximations can be very time consuming, especially for second-order derivatives based only on values of the objective function (FD= option). If analytical ...

Computing derivatives by finite difference approximations can be very time consuming, especially for second-order derivatives based only on values of the objective function (FD= option). If analytical ...

A schema combining a finite difference approach in the time direction and a spectral method in the space direction is proposed and analyzed. The main contribution of this work is threefold: 1) We ...

Convergence results for bounded time intervals are well known for finite difference approximations to the Cauchy problem for hyperbolic equations.

This paper applies a variety of second-order finite difference schemes to the SABR arbitrage-free density problem and explores alternative formulations.

This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, for parabolic partial differential equations (PDEs) of ...