Implicit schemes and LU decompositions

Journal Article · Thu Oct 01 04:00:00 EDT 1981 · Math. Comput.; (United States)

DOI:https://doi.org/10.2307/2007433· OSTI ID:5924750

Jameson, A; Turkel, E

Implicit methods for hyperbolic equations are analyzed by constructing LU factorizations. It is shown that the solution of the resulting tridiagonal systems in one dimension is well conditioned if and only if the LU factors are diagonally dominant. Stable implicit methods that have diagonally dominant factors are constructed for hyperbolic equations in n space dimesnions. Only two factors are required even in three space dimensions. Acceleration to a steady state is analyzed. When the multidimensional backward Euler method is used with large time steps, it is shown that the scheme approximates a Newton-Raphson iteration procedure.

• Research Organization: Department of Mechanical and Aeronautical Engineering, Princeton University, Princeton, New Jersey 08544
• DOE Contract Number: EY-76-C-02-3077
• OSTI ID: 5924750
• Journal Information: Math. Comput.; (United States), Journal Name: Math. Comput.; (United States) Vol. 35:156; ISSN MCMPA
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGORITHMS
DIFFERENTIAL EQUATIONS
EQUATIONS
FACTORIZATION
MANY-DIMENSIONAL CALCULATIONS
MATHEMATICAL LOGIC
NUMERICAL SOLUTION
ONE-DIMENSIONAL CALCULATIONS
PARTIAL DIFFERENTIAL EQUATIONS