We investigate the nonlinear development of a forced Rossby wave packet in the presence of a critical layer in a zonal shear flow. Most previous analyses of this phenomenon have dealt with spatially periodic, monochromatic waves. These studies observed that in the initial linear stages, the...

Incremental unknowns, earlier designed for the long-term integration of dissipative evolutionary equations, are introduced here for the incompressible Navier–Stokes equations in primitive variables when multilevel finite-difference discretizations on a staggered grid are used for the spatial...

Two new second-order finite difference techniques based upon the classical 3-point backward time centered space (BTCS) method and the Crank–Nicolson scheme, and also a fourth-order finite difference scheme based on Crandall's method for one-dimensional diffusion, are used to solve the...

A modified explicit finite difference approach to the pricing of barrier options is developed. To obtain accurate prices, the grid is constructed such that the barrier is located in a suitable position relative to horizontal layers of nodes on the grid. This means that the barrier passes through...

In this paper we study a family of finite difference schemes in two dimensions to model the single phase flow of oil through heterogeneous porous media. That family depends on one parameter θ, 0 ≤ θ ≤ 1. Using a suitable order of equations and unknowns, a linear system of equations, with a...