The analysis of the finite difference schemes with nonuniform meshes for the problems of partial differential equations is extremely rare even for very simple problems and even for the method of fully ...

In this paper, a family of new finite difference (NFD) methods for solving the convection-diffusion equation with singularly perturbed parameters are considered. By taking account of infinite terms in ...

Research from all publishers Recent studies have focused on enhancing finite difference schemes by incorporating high-order mimetic operators and curved grid techniques. For example, improvements ...

It is benchmarked against Monte Carlo simulation in the presence of a volatility skew and is shown to provide extremely accurate values for a variance swap. Our method is based on decomposing the ...