We consider a model initial and boundary value problem for the wide-angle "parabolic" equation Lu r = icu of underwater acoustics, where L is a second-order differential operator in the depth variable ...

Finite difference schemes for transient convection-diffusion problems on grids with local refinement in time and space are constructed and studied. The construction utilizes a modified upwind ...

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