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 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 ...

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 ...

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

Optical systems employ a rich array of physical effects which are described by well-understood equations. However, for all but the simplest devices these equations are typically too complex to permit ...

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 ...