TY - JOUR
T1 - Symmetric hyperbolic difference schemes and matrix problems
AU - Turkel, E.
N1 - Funding Information:
*This work was partially supported by a National Fellowship and by ERDA, contract no. E (11.1).3077.
PY - 1977
Y1 - 1977
N2 - Sufficient conditions for the stability of multidimensional finite difference schemes are difficult to obtain. It is shown that for special families of amplification matrices G (A, B) a sufficient condition for power boundedness can be obtained by replacing the matrices by appropriate scalars, and so the problem is reduced to a scalar one. As one application it is shown that the Lax-Wendroff scheme in two dimensions is stable if |Au| 2 3 + |Bu| 2 3 ≤ 1 for all real unit vectors u. The Lax- Wendroff scheme with stabilizer does not always permit such large time steps. It is conjectured that the analysis for all symmetric hyperbolic schemes can be reduced to the scalar case.
AB - Sufficient conditions for the stability of multidimensional finite difference schemes are difficult to obtain. It is shown that for special families of amplification matrices G (A, B) a sufficient condition for power boundedness can be obtained by replacing the matrices by appropriate scalars, and so the problem is reduced to a scalar one. As one application it is shown that the Lax-Wendroff scheme in two dimensions is stable if |Au| 2 3 + |Bu| 2 3 ≤ 1 for all real unit vectors u. The Lax- Wendroff scheme with stabilizer does not always permit such large time steps. It is conjectured that the analysis for all symmetric hyperbolic schemes can be reduced to the scalar case.
UR - http://www.scopus.com/inward/record.url?scp=0346236225&partnerID=8YFLogxK
U2 - 10.1016/0024-3795(77)90025-8
DO - 10.1016/0024-3795(77)90025-8
M3 - מאמר
AN - SCOPUS:0346236225
VL - 16
SP - 109
EP - 129
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
SN - 0024-3795
IS - 2
ER -