We introduce a family of recursive sequences, involving products which, for certain initial values, approximate some heavily studied rational equations. Some of the structure of solutions which hold for the rational equation but not for the associated linearized equation appear to be satisfied for the product approximation. Convergence of solutions for one particular second order member of the ...

A stable and conservative high order multi-block method for the time-dependent compressible Navier-Stokes equations has been developed. Stability and conservation are proved using summation-by-parts operators, weak interface conditions and the energy method. This development makes it possible to exploit the efficiency of the high order finite difference method for non-trivial geometries. The co...