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 ...

This paper is concerned with numerical methods for a class of two-dimensional quasilinear elliptic boundary value problems. A compact finite difference method with a nonisotropic mesh is proposed for ...

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 ...

Finite-difference approximations for the first derivative, valid halfway between equidistant gridpoints, are in general much more accurate than the corresponding approximations, which are valid at ...

This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, for parabolic partial differential equations (PDEs) of ...

A free-boundary formulation is considered for the price of American options under jump-diffusion models with finite jump activity. On the free boundary a Cauchy boundary condition holds, due to the ...