A modified Chebyshev pseudospectral method with an O(N–1) time step restriction
Journal of Computational Physics
The stability of numerical boundary treatments for compact high-order finite-difference schemes
Journal of Computational Physics
Essentially compact schemes for unsteady viscous incompressible flows
Journal of Computational Physics
Additive semi-implicit Runge-Kutta methods for computing high-speed nonequilibrium reactive flows
Journal of Computational Physics
Compact high-order accurate nonlinear schemes
Journal of Computational Physics
Higher order KFVS algorithms using compact upwind difference operators
Journal of Computational Physics
Optimized compact-difference-based finite-volume schemes for linear wave phenomena
Journal of Computational Physics
A three-point combined compact difference scheme
Journal of Computational Physics
Journal of Computational Physics
A family of high order finite difference schemes with good spectral resolution
Journal of Computational Physics
A three-point sixth-order nonuniform combined compact difference scheme
Journal of Computational Physics
High-order compact-difference schemes for time-dependent Maxwell equations
Journal of Computational Physics
Compact implicit MacCormack-type schemes with high accuracy
Journal of Computational Physics
Implicit, high-resolution, compact schemes for gas dynamics and aeroacoustics
Journal of Computational Physics
A compact-difference scheme for the Navier-Stokes equations in vorticity-velocity formulation
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Developing high-order weighted compact nonlinear schemes
Journal of Computational Physics
Prefactored small-stencil compact schemes
Journal of Computational Physics
Journal of Computational Physics
A critical evaluation of the resolution properties of B-Spline and compact finite difference methods
Journal of Computational Physics
Journal of Computational Physics
A residual-based compact scheme for the compressible Navier-Stokes equations
Journal of Computational Physics
On the use of higher-order finite-difference schemes on curvilinear and deforming meshes
Journal of Computational Physics
A simple compact fourth-order Poisson solver on polar geometry
Journal of Computational Physics
A new compact spectral scheme for turbulence simulations
Journal of Computational Physics
A fast solver of the shallow water equations on a sphere using a combined compact difference scheme
Journal of Computational Physics
Journal of Computational Physics
Compact finite difference method for American option pricing
Journal of Computational and Applied Mathematics
Development of nonlinear weighted compact schemes with increasingly higher order accuracy
Journal of Computational Physics
NPC'07 Proceedings of the 2007 IFIP international conference on Network and parallel computing
Grid stabilization of high-order one-sided differencing II: Second-order wave equations
Journal of Computational Physics
An efficient fourth-order low dispersive finite difference scheme for a 2-D acoustic wave equation
Journal of Computational and Applied Mathematics
Hi-index | 31.46 |
In this paper simple polynomial interpolation is used to derive arbitrarily high-order compact schemes for the first derivative and tridiagonal compact schemes for the second derivative (consisting of three second derivative nodes in the interior and two on the boundary) on non-uniform grids. Boundary and near boundary schemes of the same order as the interior are also developed using polynomial interpolation and for a general compact scheme on a non-uniform grid it is shown that polynomial interpolation is more efficient than the conventional method of undetermined coefficients for finding coefficients of the scheme. The high-order non-uniform schemes along with boundary closure of up to 14th order thus obtained are shown to be stable on a non-uniform grid with appropriate stretching so that more grid points are clustered near the boundary. The stability and resolution properties of the high-order non-uniform grid schemes are studied and the results of three numerical tests on stability and accuracy properties are also presented.