Murli M. Gupta

• SIAM J. Scientific Computing
• 1998
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,â€¦ (More)
• Neural Parallel & Scientific Comp.
• 2000
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 andâ€¦ (More)
In this paper, we propose a new paradigm for solving Navierâ€“Stokes equations. The proposed methodology is based on a streamfunctionâ€“velocity formulation of the two-dimensional steady-state Navierâ€“Stokes equations representing incompressible fluid flows in two-dimensional domains. Similar formulations are also possible for three-dimensional fluid flows. Theâ€¦ (More)
diffusion equations using a nine-point compact difference scheme. implementation with multigrid, and carry out a Fourier We test the efficiency of the algorithm with various smoothers and smoothing analysis of the Gaussâ€“Seidel operator. In Secintergrid transfer operators. The algorithm displays a grid-indepention 3 we present numerical experiments thatâ€¦ (More)
• Numerical Algorithms
• 2002
In this paper, we consider several finite-difference approximations for the three-dimensional biharmonic equation. A symbolic algebra package is utilized to derive a family of finite-difference approximations for the biharmonic equation on a 27 point compact stencil. The unknown solution and its first derivatives are carried as unknowns at selected gridâ€¦ (More)
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• Applied Mathematics and Computation
• 2000
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 smallerâ€¦ (More)
• 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. Weâ€¦ (More)