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 ...

A conservative difference scheme is presented for the initial-boundary value problem for generalized Zakharov equations. The scheme can be implicit or semiexplicit depending on the choice of a ...

[1] An alternating-direction hybrid implicit-explicit finite-difference time-domain method for the Schrödinger equation. Journal of Computational and Applied Mathematics (2022).

An implicit finite difference discretization is performed on time-dependent non-uniform grids. During time stepping, solutions are interpolated from one grid to another, using Lagrange interpolations.

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 ...

Explore the methodologies of the finite element method (FEM), finite difference method (FDM) and finite volume method (FVM) to grasp their computational intricacies and application-specific ...