In this paper, thirdand fourth-order compact finite difference schemes are proposed for solving Helmholtz equations with discontinuous media along straight interfaces in two space dimensions. To keep the compactness of the finite difference schemes and get global high order schemes, even at the interface where the wave number is discontinuous, the idea of the immersed interface method is employ...

This article presents a family of very high-order non-uniform grid compact finite difference schemes with spatial orders of accuracy ranging from 4th to 20th for the incompressible Navier–Stokes equations. The high-order compact schemes on non-uniform grids developed in Shukla and Zhong [R.K. Shukla, X. Zhong, Derivation of high-order compact finite difference schemes for non-uniform grid using...

We consider energy-conserving semi-discretizations of linear wave equations on nonuniform grids. Specifically we study explicit and implicit skew-adjoint finite difference methods, based on the assumption of an underlying smooth mapping from a uniform grid, applied to the first and second order wave equations. Our interest is in internal reflection of energy at abrupt variations in grid spacing...

In this paper, we study $L^p$-conjecture on locally compact hypergroups and by some technical proofs we give some sufficient and necessary conditions  for a weighted Lebesgue space  $L^p(K,w)$ to be a convolution Banach algebra, where $1<p<infty$, $K$ is a locally compact hypergroup and $w$ is a weight function on $K$.  Among the other things, we also show that if $K$ is a locally compact hyper...

in this paper high order multidimensional positive definite advection transport algorithm (mpdata) and compact finite difference methods are applied to one (1-d) and two-dimensional (2-d) advection equation. mpdata methods are designed based on upwind scheme using anti-diffusive velocity that compensates diffusivity of upwind method. in high order compact method one implicit relation between a ...