@Article{CiCP-9-4,
author = {},
title = {Exponential Compact Higher Order Scheme for Nonlinear Steady Convection-Diffusion Equations},
journal = {Communications in Computational Physics},
year = {2011},
volume = {9},
number = {4},
pages = {897--916},
abstract = {<p style="text-align: justify;">This paper presents an exponential compact higher order scheme for
Convection-Diffusion Equations (CDE) with variable and nonlinear convection coefficients. The scheme is O(h<sup>4</sup>) for one-dimensional problems and produces a tri-diagonal
system of equations which can be solved efficiently using Thomas algorithm. For two-dimensional
problems, the scheme produces an O(h<sup>4</sup>+k<sup>4</sup>) accuracy over a compact
nine point stencil which can be solved using any line iterative approach with alternate
direction implicit procedure. The convergence of the iterative procedure is guaranteed
as the coefficient matrix of the developed scheme satisfies the conditions required to
be positive. Wave number analysis has been carried out to establish that the scheme is
comparable in accuracy with spectral methods. The higher order accuracy and better
rate of convergence of the developed scheme have been demonstrated by solving numerous
model problems for one- and two-dimensional CDE, where the solutions have
the sharp gradient at the solution boundary.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.171209.300710a},
url = {https://global-sci.com/article/80875/exponential-compact-higher-order-scheme-for-nonlinear-steady-convection-diffusion-equations}
}