Implicit schemes and decompositions

Authors:
A. Jameson and E. Turkel

Journal:
Math. Comp. **37** (1981), 385-397

MSC:
Primary 65M10; Secondary 65F05

DOI:
https://doi.org/10.1090/S0025-5718-1981-0628702-9

MathSciNet review:
628702

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Abstract: 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 dimensions. 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.

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DOI:
https://doi.org/10.1090/S0025-5718-1981-0628702-9

Article copyright:
© Copyright 1981
American Mathematical Society