In this study, a high-order compact finite difference method is used to solve boundary value problems with Robin conditions. The norm use first-order scheme approximate Neumann and conditions, but that compromises the accuracy of entire scheme. As result, new higher-order schemes for approximating conditions are developed in work. Six examples testing applicability performance considered. Conve...

We derive error estimates for approximate (viscosity) solutions of Bellman equations associated to controlled jump-diffusion processes, which are fully nonlinear integro-partial differential equations. Two main results are obtained: (i) error bounds for a class of monotone approximation schemes, which includes finite difference schemes, and (ii) bounds on the error induced when the original Lév...

Abstract: In this paper, a comparison between h ig h e r order schemes has been performed in terms of numerical accuracy. Four finite difference schemes, the e xp lic it fourth-order compact Pade scheme, the implicit fourth-order Pade scheme, flowfield dependent variation (FDV) meth o d a n d h igh order compact flowfie ld dependent variation (HOC-FDV) scheme are tes ted. The FDV scheme is used...

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.

Weighted nonlinear compact schemes are ideal for simulating compressible, turbulent flows because of their nonoscillatory nature and high spectral resolution. However, they require the solution to banded systems of equations at each time-integration step or stage. We focus on tridiagonal compact schemes in this paper. We propose an efficient implementation of such schemes on massively parallel ...

Floryan, J.M. and C. Zemach, Schwarz-Christoffel methods for conformal mapping of regions with a periodic boundary, Journal of Computational and Applied Mathematics 46 (1993) 77-102. Numerical conformal mapping methods for regions with a periodic boundary have been developed. These methods are based on the generalized Schwarz-Christoffel equation and can deal with boundary curves of arbitrary f...