In this paper, third- and fourth-order compact finite difference schemes are proposed for solving Helmholtz equations with discontinuous media along straight interfaces in two space dimensions. To ...

We analyze finite difference methods for the Gross-Pitaevskii equation with an angular momentum rotation term in two and three dimensions and obtain the optimal convergence rate, for the conservative ...

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 ...

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 ...