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In this work, we use a symbolic algebra package to derive a family of nite diierence approximations for the biharmonic equation on a 9 point compact stencil. The solution and its rst derivatives are carried as unknowns at the grid points. Dirichlet boundary conditions are thus incorporatednaturally. Since the approximations use the 9 point compact stencil,… (More)

We present an explicit fourth-order compact nite diierence scheme for approximating the three dimensional convection-diiusion equation with variable coeecients. This 19-point formula is deened on a uniform cubic grid. Fourier smoothing analysis is performed to show that the smoothing factor of certain relaxation techniques used with the scheme is smaller… (More)

We combine a compact high-order diierence approximation with multigrid V-cycle algorithm to solve the two dimensional Poisson equation with Dirichlet boundary conditions. This scheme, along with several diierent orderings of grid space and projection operators, is compared with the ve-point formula to show the dramatic improvement in computed accuracy, on… (More)

In Section 2 we present the NPF difference scheme to solve the convection-diffusion equation (1), describe its We introduce a multigrid algorithm to solve the convection-diffusion equations using a nine-point compact difference scheme. We test the efficiency of the algorithm with various smoothers and smoothing analysis of the Gauss–Seidel operator. In… (More)

- Murli M. Gupta, Jun Zhang
- 1998

We present an explicit fourth-order compact nite diierence scheme for approximating the three dimensional convection-diiusion equation with variable coeecients. This 19-point formula is deened on a uniform cubic grid. Fourier smoothing analysis is performed to show that the smoothing factor of some relaxation techniques with our scheme is smaller than 1. We… (More)

We present a fourth order compact nite diierence scheme for a general three dimensional convection diiusion equation with variable coeecients on a uniform cubic grid. This high order compact diierence scheme is used to solve convection diiusion equation with boundary layers on a three dimensional nonuniform grid. We compare the computed accuracy and… (More)

Cerebral salt wasting (CSW) syndrome is an important cause of hyponatremia in head injuries apart from syndrome of inappropriate antidiuretic hormone (SIADH). Proper diagnosis and differentiation between these two entities are necessary for management as the treatment is quite opposite in both conditions. Fludrocortisone can help in managing CSW where alone… (More)

- Barbara D. Miller, Scott B. Pagel, Robert W. Rycroft, Brian L. Biles, William J. Briscoe, Michael S. Castleberry +3 others
- 2005