The complex-step method is a clever way of obtaining a numerical approximation to the first derivative of a function, avoiding the round-off error that plagues ...

Finite-Difference Time-Domain (FDTD) methods have become a cornerstone in the numerical solution of Maxwell’s equations, enabling detailed electromagnetic analysis across a wide range of applications.

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 ...

What Are FEM, FDM and FVM? FEM, FDM and FVM differ from one another in important ways. Understanding these distinctions is key to selecting the method most appropriate for your purposes. The ...