DIFFERENTIAL EQUATIONS, DIFFERENCE EQUATIONS AND MATRIX THEORY

Technical Report · Fri Nov 15 00:00:00 EST 1957

OSTI ID:4311572

Lax, P D

Friedrichs, in his studies of difference approximations to solutions of symmetric hyperbolic systems, has shown that difference schemes with positive coefficients are stable. In this paper it is shown that this stability criterion of Friedrichs is valid for difference approximations to arbitrary hyperbolic systems. The proof relies on the convexity and monotonicity of eigenvalues as matrix functions over a linear space of matrices with only real eigenvalues. These theorems, well known in the symmetric case, are proved with the aid of theorems concerning the dependence of solutions of hyperbolic equations on their initial data. (auth)

• Research Organization: New York Univ., New York. Atomic Energy Commission Computing and Applied Mathematics Center
• DOE Contract Number: AT(30-1)-1480
• NSA Number: NSA-12-004916
• OSTI ID: 4311572
• Report Number(s): NYO-7974
• Resource Relation: Other Information: Orig. Receipt Date: 31-DEC-58
• Country of Publication: United States
• Language: English

Related Subjects

PHYSICS
DIFFERENTIAL EQUATIONS
EIGENVALUES
FINITE DIFFERENCE METHOD
MATHEMATICS
MATRICES
STABILITY