We conduct experimental study on numerical solution of the two dimensional convection-diiusion equation discretized by three nite diierence schemes: the traditional central diier-ence scheme, the standard upwind scheme and the fourth-order compact scheme. We study the computed accuracy achievable by each scheme, the algebraic properties of the coeecient matrices arising from diierent schemes an...

In this paper, we extend the Sun and Zhang’s [24] work on high order finite difference method, which is based on the Richardson extrapolation technique and an operator interpolation scheme for the one and two dimensional steady convection diffusion equations to the three dimensional case. Firstly, we employ a fourth order compact difference scheme to get the fourth order accurate solution on th...

We present high-order compact schemes for a linear second-order parabolic partial differential equation (PDE) with mixed second-order derivative terms in two spatial dimensions. The schemes are applied to option pricing PDE for a family of stochastic volatility models. We use a nonuniform grid with more grid-points around the strike price. The schemes are fourth-order accurate in space and seco...

We propose a time-adaptive high-order compact finite difference scheme for option pricing in family of stochastic volatility models. employ semi-discrete method the spatial discretisation, and combine this with an adaptive time extending ideas from [LSRHF02] to fourth-order multistep methods time.

We introduce the standard fourth order compact finite difference formulae. We show how these formulae apply in the special case of the heat equation. It is well known that the American option pricing problem may be formulated in terms of the Black Scholes partial differential equation (PDE) together with a free boundary condition. Standard methods allow this problem to be transformed into a mov...