6 research outputs found
On the fourth-order accurate compact ADI scheme for solving the unsteady Nonlinear Coupled Burgers' Equations
The two-dimensional unsteady coupled Burgers' equations with moderate to
severe gradients, are solved numerically using higher-order accurate finite
difference schemes; namely the fourth-order accurate compact ADI scheme, and
the fourth-order accurate Du Fort Frankel scheme. The question of numerical
stability and convergence are presented. Comparisons are made between the
present schemes in terms of accuracy and computational efficiency for solving
problems with severe internal and boundary gradients. The present study shows
that the fourth-order compact ADI scheme is stable and efficient
Sparse grid high-order ADI scheme for option pricing in stochastic volatility models
We present a sparse grid high-order alternating direction implicit (ADI) scheme for option pricing in stochastic volatility models. The scheme is second-order in time and fourth-order in space. Numerical experiments confirm the computational efficiency gains achieved by the sparse grid combination technique