The generalized local maximum principle for a difference operator $L_h$ asserts that if $L_hu(x) > 0$ then $\Gamma u$ cannot attain its positive maximum at the net ...

Finite difference methods have become a cornerstone in the simulation of seismic wave propagation, providing a robust numerical framework to approximate the differential equations that govern seismic ...

Boundary value problems for singularly perturbed semilinear elliptic equations are considered. Special piecewise-uniform meshes are constructed which yield accurate numerical solutions irrespective of ...

First-order derivatives: n additional function calls are needed. Second-order derivatives based on gradient calls, when the "grd" module is specified (Dennis and Schnabel 1983): n additional gradient ...

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 ...

The FD= and FDHESSIAN= options specify the use of finite difference approximations of the derivatives. The FD= option specifies that all derivatives are approximated using function evaluations, and ...