Accession Number:

AD0718058

Title:

Third and Fourth Order Accurate Schemes for Hyperbolic Equations of Conservation Law Form

Descriptive Note:

Corporate Author:

TEL-AVIV UNIV (ISRAEL) DEPT OF MATHEMATICAL SCIENCES

Personal Author(s):

Report Date:

1970-04-01

Pagination or Media Count:

18.0

Abstract:

It is shown that for quasi-linear hyperbolic systems of the conservation form W sub t -F sub x -AW sub x, it is possible to build up relatively simple finite difference numerical schemes accurate to 3rd and 4th order provided that the matrix A satisfies commutativity relations with its partial-derivative-matrices. This requirement is not fulfilled by any known physical systems of equations. These schemes generalize the Lax-Wendroff 2nd order one, and are written down explicitly. As found by Strang, odd order schemes are linearly unstable unless modified by adding a term containing the next higher space derivative. Thus stabilized, the schemes, both odd and even, can be made to meet the C.F.L. Courant-Friedrichs-Lewy criterion. Numerical calculations were made with a 3rd order and a 4th order scheme for scalar equations with continuous and discontinuous solutions. The results are compared with analytic solutions and the predicted improvement is verified.

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE