@TechReport{ it:2010-023,
author = {Ken Mattsson},
title = {Summation by Parts Operators for Finite Difference
Approximations of Second-Derivatives with Variable
Coefficients},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2010},
number = {2010-023},
month = oct,
abstract = {Finite difference operators approximating second
derivatives with variable coefficients and satisfying a
summation-by-parts rule have been derived for the second-,
fourth- and sixth-order case by using the symbolic
mathematics software Maple. The operators are based on the
same norms as the corresponding approximations of the first
derivate, which makes the construction of stable
approximations to general multi-dimensional
hyperbolic-parabolic problems straightforward.}
}