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 ...

Mathematical approaches for numerically solving partial differential equations. The focus will be (a) iterative solution methods for linear and non-linear equations, (b) spatial discretization and ...

We develop here a finite-difference approach for valuing a discretely sampled variance swap within an extended Black–Scholes framework. This approach incorporates the observed volatility skew and is ...