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.

In this paper, we give sixth order compact finite difference formula for second order integro-differential equations (IDE) with different boundary conditions, and both of error estimates and numerical experiments confirm our compact finite difference method can get fifth order of accuracy. We also adjust compact finite difference method for first order IDE and a system of IDE and give numerical...

A finite compact (FC) difference scheme requiring only bi-diagonal matrix inversion is proposed by using the known high-resolution flux. Introducing TVD or ENO limiters in the numerical flux, several high-resolution FC-schemes of hyperbolic conservation law are developed, including the FC-TVD, third-order FC-ENO and fifth-order FC-ENO schemes. Boundary conditions formulated need only one unknow...

A stable high order finite difference with a fully implicit time-marching scheme is proposed to solve the two-dimensional unsteady convection diffusion equation with variable coefficients. It is essentially compact and has the nice features of a compact scheme with regard to the treatment of boundary conditions. A time-dependent multigrid full approximation storage(FAS) scheme , which is suitab...

This study proposes one-dimensional advection–diffusion equation (ADE) with finite differences method (FDM) using implicit spreadsheet simulation (ADEISS). By changing only the values of temporal and spatial weighted parameters with ADEISS implementation, solutions are implicitly obtained for the BTCS, Upwind and Crank–Nicolson schemes. The ADEISS uses iterative spreadsheet solution technique. ...