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Summation by Parts Operators for Finite Difference Approximations of Second-Derivatives with Variable Coefficients

Summation by Parts Operators for Finite Difference Approximations of Second-Derivatives with... 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 derivative, which makes the construction of stable approximations to general multi-dimensional hyperbolic-parabolic problems straightforward. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Scientific Computing Springer Journals

Summation by Parts Operators for Finite Difference Approximations of Second-Derivatives with Variable Coefficients

Journal of Scientific Computing , Volume 51 (3) – Sep 3, 2011

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References (42)

Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer Science+Business Media, LLC
Subject
Mathematics; Appl.Mathematics/Computational Methods of Engineering; Algorithms; Theoretical, Mathematical and Computational Physics; Computational Mathematics and Numerical Analysis
ISSN
0885-7474
eISSN
1573-7691
DOI
10.1007/s10915-011-9525-z
Publisher site
See Article on Publisher Site

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 derivative, which makes the construction of stable approximations to general multi-dimensional hyperbolic-parabolic problems straightforward.

Journal

Journal of Scientific ComputingSpringer Journals

Published: Sep 3, 2011

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