Nature

Adaptive finite differencing in high accuracy electronic structure calculations

A multi-order Adaptive Finite Differencing (AFD) method is developed for the kinetic energy operator in real-space, grid-based electronic structure codes. It uses atomic pseudo orbitals produced by ...
Nature

Development of a fourth-order compact finite difference scheme for simulation of simulated ...

$$\frac{\partial c}{\partial t}+v\frac{\partial c}{\partial x}={D}_{{\rm{a}}}+\frac{{\partial }^{2}c}{\partial {x}^{2}}-\frac{1-{\varepsilon }_{{\rm{b ...
Risk

Finite-difference solution ansatz approach in least-squares Monte Carlo

This paper presents a simple but effective and efficient approach to improve the accuracy and stability of the least-squares Monte Carlo method. The key idea is to construct an ansatz for the ...
Risk

Finite difference schemes with exact recovery of vanilla option prices

Peter Austing shows how to set up finite difference solvers to exactly recover the prices of all vanilla options on the grid. The approach leads to a specific discretisation of Dupire’s formula. It ...